{"id":15803,"date":"2024-02-29T05:44:34","date_gmt":"2024-02-29T00:14:34","guid":{"rendered":"https:\/\/www.aplustopper.com\/?p=15803"},"modified":"2024-02-29T14:59:59","modified_gmt":"2024-02-29T09:29:59","slug":"selina-icse-solutions-class-10-maths-circles","status":"publish","type":"post","link":"https:\/\/www.aplustopper.com\/selina-icse-solutions-class-10-maths-circles\/","title":{"rendered":"Selina Concise Mathematics Class 10 ICSE Solutions Circles"},"content":{"rendered":"

Selina Concise Mathematics Class 10 ICSE Solutions Circles<\/h2>\n

Selina Publishers Concise Mathematics Class 10 ICSE Solutions Chapter 17 Circles<\/strong><\/p>\n

Circles Exercise 17A – Selina Concise Mathematics Class 10 ICSE Solutions<\/h3>\n

Circles Class 10\u00a0Question 1.<\/span>
\nIn the given figure, O is the centre of the circle. \u2220OAB and \u2220OCB are 30\u00b0 and 40\u00b0 respectively. Find \u2220AOC. Show your steps of working.
\n\"Selina
\nSolution:<\/span>
\n\"Selina<\/p>\n

Question 2.<\/span>
\nIn the given figure, \u2220BAD = 65\u00b0, \u2220ABD = 70\u00b0, \u2220BDC = 45\u00b0
\n(i) Prove that AC is a diameter of the circle.
\n(ii) Find \u2220ACB.
\n\"Selina
\nSolution:<\/span>
\n\"Selina<\/p>\n

Question 3.<\/span>
\nGiven O is the centre of the circle and \u2220AOB = 70\u00b0. Calculate the value of:
\n(i) \u2220 OCA,
\n(ii) \u2220OAC.
\n\"Selina
\nSolution:<\/span>
\n\"Selina<\/p>\n

Question 4.<\/span>
\nIn each of the following figures, O is the centre of the circle. Find the values of a, b, and c.
\n\"Selina
\nSolution:<\/span>
\n\"Selina<\/p>\n

Question 5.<\/span>
\nIn each of the following figures, O is the centre of the circle. Find the value of a, b, c and d.
\n\"Selina
\nSolution:<\/span>
\n\"Selina
\n\"Selina<\/p>\n

Question 6.<\/span>
\nIn the figure, AB is common chord of the two circles. If AC and AD are diameters; prove that D, B and C are in a straight line. O1<\/sub> and O2<\/sub> are the centres of two circles.
\n\"Selina
\nSolution:<\/span>
\n\"Selina<\/p>\n

Question 7.<\/span>
\nIn the figure given beow, find :
\n(i) \u2220 BCD,
\n(ii) \u2220 ADC,
\n(iii) \u2220 ABC.
\n\"Selina
\nShow steps of your workng.
\nSolution:<\/span>
\n\"Selina<\/p>\n

Question 8.<\/span>
\nIn the given figure, O is centre of the circle. If \u2220 AOB = 140\u00b0 and \u2220 OAC = 50\u00b0; find :
\n(i) \u2220 ACB,
\n(ii) \u2220 OBC,
\n(iii) \u2220 OAB,
\n(iv) \u2220CBA
\n\"Selina
\nSolution:<\/span>
\n\"Selina<\/p>\n

Question 9.<\/span>
\nCalculate :
\n(i) \u2220 CDB,
\n(ii) \u2220 ABC,
\n(iii) \u2220 ACB.
\n\"Selina
\nSolution:<\/span>
\n\"Selina<\/p>\n

Question 10.<\/span>
\nIn the figure given below, ABCD is a eyclic quadrilateral in which \u2220 BAD = 75\u00b0; \u2220 ABD = 58\u00b0 and \u2220ADC = 77\u00b0. Find:
\n(i) \u2220 BDC,
\n(ii) \u2220 BCD,
\n(iii) \u2220 BCA.
\n\"Selina
\nSolution:<\/span>
\n\"Selina<\/p>\n

Question 11.<\/span>
\nIn the following figure, O is centre of the circle and \u2206 ABC is equilateral. Find :
\n(i) \u2220 ADB
\n(ii) \u2220 AEB
\n\"Selina
\nSolution:<\/span>
\n\"Selina<\/p>\n

Question 12.<\/span>
\nGiven\u2014\u2220 CAB = 75\u00b0 and \u2220 CBA = 50\u00b0. Find the value of \u2220 DAB + \u2220 ABD
\n\"Selina
\nSolution:<\/span>
\n\"Selina<\/p>\n

Question 13.<\/span>
\nABCD is a cyclic quadrilateral in a circle with centre O.
\nIf \u2220 ADC = 130\u00b0; find \u2220 BAC.
\n\"Selina
\nSolution:<\/span>
\n\"Selina<\/p>\n

Question 14.<\/span>
\nIn the figure given below, AOB is a diameter of the circle and \u2220 AOC = 110\u00b0. Find \u2220 BDC.
\n\"Selina
\nSolution:<\/span>
\n\"Selina<\/p>\n

Question 15.<\/span>
\nIn the following figure, O is centre of the circle,
\n\u2220 AOB = 60\u00b0 and \u2220 BDC = 100\u00b0.
\nFind \u2220 OBC.
\n\"Selina<\/p>\n

Solution:<\/span>
\n\"Selina<\/p>\n

Question 16.<\/span>
\nABCD is a cyclic quadrilateral in which \u2220 DAC = 27\u00b0; \u2220 DBA = 50\u00b0 and \u2220 ADB = 33\u00b0.
\nCalculate :
\n(i) \u2220 DBC,
\n(ii) \u2220 DCB,
\n(iii) \u2220 CAB.
\n\"Selina
\nSolution:<\/span>
\n\"Selina<\/p>\n

Question 17.<\/span>
\nIn the figure given alongside, AB and CD are straight lines through the centre O of a circle. If \u2220AOC = 80\u00b0 and \u2220CDE = 40\u00b0. Find the number of degrees in:
\n(i) \u2220DCE;
\n(ii) \u2220ABC.
\n\"Selina
\nSolution:<\/span>
\n\"Selina<\/p>\n

Question 17 (old).<\/span>
\nIn the figure given below, AB is diameter of the circle whose centre is O. Given that:
\n\u2220 ECD = \u2220 EDC = 32\u00b0.
\n\"Selina
\nShow that \u2220 COF = \u2220 CEF.
\nSolution:<\/span>
\n\"Selina<\/p>\n

Question 18.<\/span>
\nIn the figure given below, AC is a diameter of a circle, whose centre is O. A circle is described on AO as diameter. AE, a chord of the larger circle, intersects the smaller circle at B. Prove that AB = BE.
\n\"Selina
\nSolution:<\/span>
\n\"Selina<\/p>\n

Question 19.<\/span>
\nIn the following figure,
\n(i) if \u2220BAD = 96\u00b0, find BCD and
\n(ii) Prove that AD is parallel to FE.
\n\"Selina
\nSolution:<\/span>
\n\"Selina<\/p>\n

Question 20.<\/span>
\nProve that:
\n(i) the parallelogram, inscribed in a circle, is a rectangle.
\n(ii) the rhombus, inscribed in a circle, is a square.
\nSolution:<\/span>
\n\"Selina
\n\"Selina<\/p>\n

Question 21.<\/span>
\nIn the following figure, AB = AC. Prove that DECB is an isosceles trapezium.
\n\"Selina
\nSolution:<\/span>
\n\"Selina<\/p>\n

Question 22.<\/span>
\nTwo circles intersect at P and Q. Through P diameters PA and PB of the two circles are drawn. Show that the points A, Q and B are collinear.
\nSolution:<\/span>
\n\"Selina<\/p>\n

Question 23.<\/span>
\nThe figure given below, shows a circle with centre O. Given: \u2220 AOC = a and \u2220 ABC = b.
\n(i) Find the relationship between a and b
\n(ii) Find the measure of angle OAB, if OABC is a parallelogram.
\n\"Selina
\nSolution:<\/span>
\n\"Selina<\/p>\n

Question 24.<\/span>
\nTwo chords AB and CD intersect at P inside the circle. Prove that the sum of the angles subtended by the arcs AC and BD as the centre O is equal to twice the angle APC.
\nSolution:<\/span>
\n\"Selina<\/p>\n

Question 24 (old).<\/span>
\nABCD is a quadrilateral inscribed in a circle having \u2220A = 60\u00b0; O is the centre of the circle. Show that: \u2220OBD + \u2220ODB = \u2220CBD + \u2220CDB
\nSolution:<\/span>
\n\"Selina<\/p>\n

Question 25.<\/span>
\nIn the figure given RS is a diameter of the circle. NM is parallel to RS and \u2220MRS = 29\u00b0
\nCalculate:
\n(i) \u2220RNM;
\n(ii) \u2220NRM.
\n\"Selina
\nSolution:<\/span>
\n\"Selina<\/p>\n

Question 26.<\/span>
\nIn the figure given alongside, AB || CD and O is the centre of the circle. If \u2220 ADC = 25\u00b0; find the angle AEB. Give reasons in support of your answer.
\n\"Selina
\nSolution:<\/span>
\n\"Selina<\/p>\n

Question 27.<\/span>
\nTwo circles intersect at P and Q. Through P, a straight line APB is drawn to meet the circles in A and B. Through Q, a straight line is drawn to meet the circles at Cand D. Prove that AC is parallel to BD.
\n\"Selina
\nSolution:<\/span>
\n\"Selina<\/p>\n

Question 28.<\/span>
\nABCD is a cyclic quadrilateral in which AB and DC on being produced, meet at P such that PA = PD. Prove that AD is parallel to BC.
\nSolution:<\/span>
\n\"Selina<\/p>\n

Question 29.<\/span>
\nAB is a diameter of the circle APBR as shown in the figure. APQ and RBQ are straight lines. Find:
\n(i) \u2220PRB
\n(ii) \u2220PBR
\n(iii) \u2220BPR.
\n\"Selina
\nSolution:<\/span>
\n\"Selina<\/p>\n

Question 30.<\/span>
\nIn the given figure, SP is the bisector of angle RPT and PQRS is a cyclic quadrilateral. Prove that: SQ = SR.
\n\"Selina
\nSolution:<\/span>
\n\"Selina<\/p>\n

Question 31.<\/span>
\nIn the figure, O is the centre of the circle, \u2220AOE = 150\u00b0, DAO = 51\u00b0. Calculate the sizes of the angles CEB and OCE.
\n\"Selina
\nSolution:<\/span>
\n\"Selina<\/p>\n

Question 32.<\/span>
\nIn the figure, P and Q are the centres of two circles intersecting at B and C. ACD is a straight line. Calculate the numerical value of x.
\n\"Selina
\nSolution:<\/span>
\n\"Selina<\/p>\n

Question 33.<\/span>
\nThe figure shows two circles which intersect at A and B. The centre of the smaller circle is O and lies on the circumference of the larger circle. Given that \u2220APB = a\u00b0. Calculate, in terms of a\u00b0, the value of:
\n(i) obtuse \u2220AOB
\n(ii) \u2220ACB
\n(iii) \u2220ADB.
\nGive reasons for your answers clearly.
\n\"Selina
\nSolution:<\/span>
\n\"Selina<\/p>\n

Question 34.<\/span>
\nIn the given figure, O is the centre of the circle and \u2220 ABC = 55\u00b0. Calculate the values of x and y.
\n\"Selina
\nSolution:<\/span>
\n\"Selina<\/p>\n

Question 35.<\/span>
\nIn the given figure, A is the centre of the circle, ABCD is a parallelogram and CDE is a straight line. Prove that \u2220BCD = 2\u2220ABE
\n\"Selina
\nSolution:<\/span>
\n\"Selina<\/p>\n

Question 36.<\/span>
\nABCD is a cyclic quadrilateral in which AB is parallel to DC and AB is a diameter of the circle. Given \u2220BED = 65\u00b0; calculate:
\n(i) \u2220 DAB,
\n(ii) \u2220BDC.
\n\"Selina
\nSolution:<\/span>
\n\"Selina<\/p>\n

Question 37.<\/span>
\n\u2220 In the given figure, AB is a diameter of the circle. Chord ED is parallel to AB and \u2220 EAB = 63\u00b0; calculate:
\n(i) \u2220EBA,
\n(ii) BCD.
\n\"Selina
\nSolution:<\/span>
\n\"Selina<\/p>\n

Question 38.<\/span>
\nIn the given figure, AB is a diameter of the circle with centre O. DO is parallel to CB and \u2220DCB = 120\u00b0; calculate:
\n(i) \u2220 DAB,
\n(ii) \u2220 DBA,
\n(iii) \u2220 DBC,
\n(iv) \u2220 ADC.
\nAlso, show that the \u2206AOD is an equilateral triangle.
\n\"Selina
\nSolution:<\/span>
\n\"Selina<\/p>\n

Question 39.<\/span>
\nIn the given figure, I is the incentre of the \u2206 ABC. Bl when produced meets the circumcirle of \u2206 ABC at D. Given \u2220BAC = 55\u00b0 and \u2220 ACB = 65\u00b0, calculate:
\n(i) \u2220DCA,
\n(ii) \u2220 DAC,
\n(iii) \u2220DCI,
\n(iv) \u2220AIC.
\n\"Selina
\nSolution:<\/span>
\n\"Selina<\/p>\n

Question 40.<\/span>
\nA triangle ABC is inscribed in a circle. The bisectors of angles BAC, ABC and ACB meet the circumcircle of the triangle at points P, Q and R respectively. Prove that:
\n(i) \u2220ABC = 2 \u2220APQ
\n(ii) \u2220ACB = 2 \u2220APR
\n(iii) \u2220QPR = 90\u00b0 – \\(\\frac{1}{2}\\)BAC
\n\"Selina
\nSolution:<\/span>
\n\"Selina<\/p>\n

Question 40 (old).<\/span>
\nThe sides AB and DC of a cyclic quadrilateral ABCD are produced to meet at E; the sides DA and CB are produced to meet at F. If \u2220BEC = 42\u00b0 and \u2220BAD = 98\u00b0; calculate:
\n(i) \u2220AFB,
\n(ii) \u2220ADC.
\n\"Selina
\nSolution:<\/span>
\n\"Selina<\/p>\n

Question 41.<\/span>
\nCalculate the angles x, y and z if: \\(\\frac{x}{3}=\\frac{y}{4}=\\frac{z}{5}\\)
\n\"Selina
\nSolution:<\/span>
\n\"Selina<\/p>\n

Question 42.<\/span>
\nIn the given figure, AB = AC = CD and \u2220ADC = 38\u00b0. Calculate:
\n(i) Angle ABC
\n(ii) Angle BEC.
\n\"Selina
\nSolution:<\/span>
\n\"Selina<\/p>\n

Question 43.<\/span>
\nIn the given figure, AC is the diameter of circle, centre O. Chord BD is perpendicular to AC. Write down the angles p, and r in terms of x.
\n\"Selina
\nSolution:<\/span>
\n\"Selina<\/p>\n

Question 44.<\/span>
\nIn the given figure, AC is the diameter of circle, centre O. CD and BE are parallel. Angle AOB = 80\u00b0 and angle ACE = 10\u00b0. Calculate:
\n(i) Angle BEC;
\n(ii) Angle BCD;
\n(iii) Angle CED.
\n\"Selina
\nSolution:<\/span>
\n\"Selina<\/p>\n

Question 45.<\/span>
\nIn the given figure, AE is the diameter of circle. Write down the numerical value of \u2220ABC + \u2220CDE. Give reasons for your answer.
\n\"Selina
\nSolution:<\/span>
\n\"Selina<\/p>\n

Question 46.<\/span>
\nIn the given figure, AOC is a diameter and AC is parallel to ED. If \u2220CBE = 64\u00b0, calculate \u2220DEC.
\n\"Selina
\nSolution:<\/span>
\n\"Selina<\/p>\n

Question 47.<\/span>
\nUse the given figure to find
\n(i) \u2220BAD
\n(ii) \u2220DQB.
\n\"Selina
\nSolution:<\/span>
\n\"Selina<\/p>\n

Question 48.<\/span>
\nIn the given figure, AOB is a diameter and DC is parallel to AB. If \u2220 CAB = x\u00b0; find (in terms of x) the values of:
\n(i) \u2220COB
\n(ii) \u2220DOC
\n(iii) \u2220DAC
\n(iv) \u2220ADC.
\n\"Selina
\nSolution:<\/span>
\n\"Selina<\/p>\n

Question 49.<\/span>
\nIn the given figure, AB is the diameter of a circle with centre O. \u2220BCD = 130\u00b0. Find:
\n(i) \u2220DAB
\n(ii) \u2220DBA
\n\"Selina
\nSolution:<\/span>
\n\"Selina<\/p>\n

Question 50.<\/span>
\nIn the given figure, PQ is the diameter of the circle whose centre is O. Given \u2220ROS = 42\u00b0; calculate \u2220RTS.
\n\"Selina
\nSolution:<\/span>
\n\"Selina<\/p>\n

Question 51.<\/span>
\nIn the given figure, PQ is a diameter. Chord SR is parallel to PQ. Given that \u2220PQR = 58\u00b0; calculate
\n(i) \u2220RPQ
\n(ii) \u2220STP.
\n\"Selina
\nSolution:<\/span>
\n\"Selina<\/p>\n

Question 52.<\/span>
\nAOD = 60\u00b0; calculate the numerical values of:
\nAB is the diameter of the circle with centre O. OD is parallel to BC and \u2220AOD = 60\u00b0; calculate the numerical values of:
\n(i) \u2220ABD,
\n(ii) \u2220DBC,
\n(iii) \u2220ADC.
\n\"Selina
\nSolution:<\/span>
\n\"Selina<\/p>\n

Question 53.<\/span>
\nIn the given figure, the centre of the small circle lies on the circumference of the bigger circle. If \u2220APB = 75\u00b0 and \u2220BCD = 40″; find:
\n(i) \u2220AOB,
\n(ii) \u2220ACB,
\n(iii) \u2220ABD,
\n(iv) \u2220ADB.
\n\"Selina
\nSolution:<\/span>
\n\"Selina<\/p>\n

Question 54.<\/span>
\nIn the given figure, \u2220BAD = 65\u00b0, \u2220ABD = 70\u00b0 and \u2220BDC = 45\u00b0; find:
\n(i) \u2220BCD,
\n(ii) \u2220ACB.
\nHence, show that AC is a diameter.
\n\"Selina
\nSolution:<\/span>
\n\"Selina<\/p>\n

Question 55.<\/span>
\nIn a cyclic quadrilateral ABCD, \u2220A : \u2220C = 3 : 1 and \u2220B : \u2220D = 1 : 5; find each angle of the quadrilateral.
\nSolution:<\/span>
\n\"Selina<\/p>\n

Question 56.<\/span>
\nThe given figure shows a circle with centre O and \u2220ABP = 42\u00b0. Calculate the measure of
\n(i) \u2220PQB
\n(ii) \u2220QPB + \u2220PBQ
\n\"Selina
\nSolution:<\/span>
\n\"Selina<\/p>\n

Question 57.<\/span>
\nIn the given figure, M is the centre of the circle. Chords AB and CD are perpendicular to each other. If \u2220 MAD =x and \u2220BAC = y.
\n(i) express \u2220AMD in terms of x.
\n(ii) express \u2220ABD in terms of y.
\n(iii) prove that : x = y
\n\"Selina
\nSolution:<\/span>
\n\"Selina<\/p>\n

Question 61 (old).<\/span>
\nIn a circle, with centre O, a cyclic quadrilateral ABCD is drawn with AB as a diameter of the circle and CD equal to radius of the circle. If AD and BC produced meet at point P; show that \u2220APB = 60\u00b0.
\nSolution:<\/span>
\n\"Selina<\/p>\n

Circles Exercise 17B – Selina Concise Mathematics Class 10 ICSE Solutions<\/h3>\n

Question 1.<\/span>
\nIn a cyclic-trapezium, the non-parallel sides are equal and the diagonals are also equal.
\nProve it.
\nSolution:<\/span>
\n\"Selina<\/p>\n

Question 2.<\/span>
\nIn the following figure, AD is the diameter of the circle with centre 0. chords AB, BC and CD are equal. If \u2220DEF = 110\u00b0, calculate:
\n(i) \u2220 AFE,
\n(ii) \u2220FAB.
\n\"Selina<\/p>\n

Solution:<\/span>
\n\"Selina<\/p>\n

Question 3.<\/span>
\nIf two sides of a cycli-quadrilateral are parallel; prove thet:
\n(i) its other two side are equal.
\n(ii) its diagonals are equal.
\nSolution:<\/span>
\n\"Selina<\/p>\n

Question 4.<\/span>
\nThe given figure show a circle with centre O. also, PQ = QR = RS and \u2220PTS = 75\u00b0. Calculate:
\n(i) \u2220POS,
\n(ii) \u2220 QOR,
\n(iii) \u2220PQR.
\n\"Selina
\nSolution:<\/span>
\n\"Selina<\/p>\n

Question 5.<\/span>
\nIn the given figure, AB is a side of a regular six-sided polygon and AC is a side of a regular eight-sided polygon inscribed in the circle with centre O. calculate the sizes of:
\n(i) \u2220 AOB,
\n(ii) \u2220 ACB,
\n(iii) \u2220ABC.
\n\"Selina
\nSolution:<\/span>
\n\"Selina<\/p>\n

Question 6.<\/span>
\nIn a regular pentagon ABCDE, inscribed in a circle; find ratio between angle EDA and angel ADC.
\nSolution:<\/span>
\n\"Selina<\/p>\n

Question 7.<\/span>
\nIn the given figure. AB = BC = CD and \u2220ABC = 132\u00b0, calculate:
\n(i) \u2220AEB,
\n(ii) \u2220 AED,
\n(iii) \u2220COD.
\n\"Selina
\nSolution:<\/span>
\n\"Selina<\/p>\n

Question 8.<\/span>
\nIn the figure, O is the centre of the circle and the length of arc AB is twice the length of arc BC. If angle AOB = 108\u00b0, find:
\n(i) \u2220 CAB,
\n(ii) \u2220ADB.
\n\"Selina
\nSolution:<\/span>
\n\"Selina<\/p>\n

Question 9.<\/span>
\nThe figure shows a circle with centre O. AB is the side of regular pentagon and AC is the side of regular hexagon. Find the angles of triangle ABC.
\n\"Selina
\nSolution:<\/span>
\n\"Selina<\/p>\n

Question 10.<\/span>
\nIn the given figire, BD is a side of a regularhexagon, DC is a side of a regular pentagon and AD is adiameter. Calculate:
\n(i) \u2220 ADC
\n(ii) \u2220BAD,
\n(iii) \u2220ABC
\n(iv) \u2220 AEC.
\n\"Selina
\nSolution:<\/span>
\n\"Selina
\n\"Selina<\/p>\n

Circles Exercise 17C – Selina Concise Mathematics Class 10 ICSE Solutions<\/h3>\n

Question 1.
\n<\/span>In the given circle with diametre AB, find the value of x.<\/p>\n

\"Selina
\nSolution:<\/span>
\n\"Selina
\n\u2220ABD = \u2220ACD = 30\u00b0 (Angle in the same segment)
\nNow in \u2206 ADB,
\n\u2220BAD + \u2220ADB + \u2220DBA = 180\u00b0\u00a0(Angles of a A)
\nBut \u2220ADB = 90\u00b0 (Angle in a semi-circle)
\n\u2234 x + 90\u00b0 + 30\u00b0 = 180\u00b0 \u21d2 x + 120\u00b0 = 180\u00b0
\n\u2234 x= 180\u00b0 – 120\u00b0 = 60\u00b0 Ans.<\/p>\n

Question 1.<\/span>
\nIn the given figure, O is the centre of the circle with radius 5 cm, OP and OQ are perpendiculars to AB and CD respectively. AB = 8cm and CD = 6cm. Determine the length of PQ.
\n\"Selina
\nSolution:<\/span><\/p>\n

\"Selina<\/p>\n

Question 2.<\/span>
\nIn the given figure, ABC is a triangle in which \u2220 BAC = 30\u00b0 Show that BC is equal to the radius of the circum-circle of the triangle ABC, whose centre is O.
\n\"Selina
\nSolution:<\/span>
\n\"Selina<\/p>\n

Question 3.<\/span>
\nProve that the circle drawn on any one a the equalside of an isoscele triangle as diameter bisects the base.
\nSolution:<\/span>
\n\"Selina<\/p>\n

Question 3 (old).<\/span>
\nThe given figure show two circles with centres A and B; and radii 5 cm and 3cm respectively, touching each other internally. If the perpendicular bisector of AB meets the bigger circle in P and Q, find the length of PQ.
\n\"Selina
\nSolution:<\/span>
\n\"Selina<\/p>\n

Question 4.<\/span>
\nIn the given figure, chord ED is parallel to diameter AC of the circle. Given \u2220 CBE = 65\u00b0, calculate \u2220DEC.
\n\"Selina
\nSolution:<\/span>
\n\"Selina<\/p>\n

Question 5.<\/span>
\nThe quadrilateral formed by angle bisectors of a cyclic quadrilateral is also cyclic. Prove it.
\nSolution:<\/span>
\n\"Selina<\/p>\n

Question 6.<\/span>
\nIn the figure, \u2220DBC = 58\u00b0. BD is a diameter of the circle. Calculate:
\n(i) \u2220BDC
\n(ii) \u2220BEC
\n(iii) \u2220BAC
\n\"Selina
\nSolution:<\/span>
\n\"Selina<\/p>\n

Question 7.<\/span>
\nD and E are points on equal sides AB and AC of an isosceles triangle ABC such that AD = AE. Provet that the points B, C, E and D are concyclic.
\nSolution:<\/span>
\n\"Selina<\/p>\n

Question 7 (old).<\/span>
\nChords AB and CD of a circle intersect each other at point P such that AP = CP.
\nShow that: AB = CD.
\n\"Selina
\nSolution:<\/span>
\n\"Selina<\/p>\n

Question 8.<\/span>
\nIn the given rigure, ABCD is a cyclic eqadrilateral. AF is drawn parallel to CB and DA is produced to point E. If \u2220 ADC = 92\u00b0, \u2220 FAE = 20\u00b0; determine \u2220 BCD. Given reason in support of your answer.
\n\"Selina
\nSolution:<\/span>
\n\"Selina<\/p>\n

Question 9.<\/span>
\nIf I is the incentre of triangle ABC and Al when produced meets the cicrumcircle of triangle ABC in points D. if \u2220 BAC = 66\u00b0 and \u2220 = 80o.calculate:
\n(i) \u2220 DBC
\n(ii) \u2220 IBC
\n(iii) \u2220 BIC.
\n\"Selina
\nSolution:<\/span>
\n\"Selina
\n\"Selina<\/p>\n

Question 10.<\/span>
\nIn the given figure, AB = AD = DC = PB and \u2220 DBC = x\u00b0. Determine, in terms of x:
\n(i) \u2220 ABD,
\n(ii) \u2220 APB.
\nHence or otherwise, prove thet AP is parallel to DB.
\n\"Selina
\nSolution:<\/span>
\n\"Selina<\/p>\n

Question 11.<\/span>
\nIn the given figure; ABC, AEQ and CEP are straight lines. Show that \u2220APE and \u2220 CQE are supplementary.
\n\"Selina
\nSolution:<\/span>
\n\"Selina<\/p>\n

Question 12.<\/span>
\nIn the given, AB is the diameter of the circle with centre O.
\n\"Selina
\nIf \u2220 ADC = 32\u00b0, find angle BOC.
\nSolution:<\/span>
\n\"Selina<\/p>\n

Question 13.<\/span>
\nIn a cyclic-quadrilateral PQRS, angle PQR = 135\u00b0. Sides SP and RQ prouduced meet at point A: whereas sides PQ and SR produced meet at point B.
\nIf \u2220A: \u2220B = 2 : 1;find angles A and B.
\nSolution:<\/span>
\n\"Selina
\n\"Selina<\/p>\n

Question 17 (old).<\/span>
\nIf the following figure, AB is the diameter of a circle with centre O and CD is the chord with lengh equal radius OA.
\nIf AC produced and BD produed meet at point p; show that \u2220APB = 60\u00b0
\n\"Selina
\nSolution:<\/span>
\n\"Selina
\n\"Selina<\/p>\n

Question 14.<\/span>
\nIn the following figure, ABCD is a cyclic quadrilateral in which AD is parallel to BC.
\n\"Selina
\nIf the bisector of angle A meet BC at point E and the given circle at point F, prove that:
\n(i) EF = FC
\n(ii) BF =DF
\nSolution:<\/span>
\n\"Selina<\/p>\n

Question 15.<\/span>
\nABCD is a cyclic quadrilateral. Sides AB and DC produced meet at point e; whereas sides BC and AD produced meet at point F. I f \u2220 DCF : \u2220F : \u2220E = 3 : 5 : 4, find the angles of the cyclic quadrilateral ABCD.
\nSolution:<\/span>
\n\"Selina
\n\"Selina<\/p>\n

Question 16.<\/span>
\nThe following figure shows a cicrcle with PR as its diameter. If PQ = 7 cm and QR = 3RS = 6 cm, Find the perimetre of the cyclic quadrilateral PORS.
\n\"Selina
\nSolution:<\/span>
\n\"Selina<\/p>\n

Question 17.<\/span>
\nIn the following figure, AB is the diameter of a circle with centre O. If chord AC = chord AD.prove that:
\n(i) arc BC = arc DB
\n(ii) AB is bisector of \u2220 CAD.
\nFurther if the lenghof arc AC is twice the lengthof arc BC find :
\n(a) \u2220 BAC
\n(b) \u2220 ABC
\n\"Selina
\nSolution:<\/span>
\n\"Selina
\n\"Selina<\/p>\n

Question 18.<\/span>
\nIn cyclic quadrilateral ABCD; AD = BC, \u2220 = 30\u00b0 and \u2220 = 70\u00b0; find;
\n(i) \u2220 BCD
\n(ii) \u2220BCA
\n(iii) \u2220ABC
\n(iv) \u2220 ADC
\nSolution:<\/span>
\n\"Selina
\n\"Selina<\/p>\n

Question 19.<\/span>
\nIn the given figure, \u2220ACE = 43\u00b0 and \u2220 = 62\u00b0; find the values of a, b and c.
\n\"Selina
\nSolution:<\/span>
\n\"Selina<\/p>\n

Question 20.<\/span>
\nIn the given figure, AB is parallel to DC, \u2220BCE = 80\u00b0 and \u2220 BAC = 25\u00b0
\nFind
\n(i) \u2220 CAD
\n(ii) \u2220 CBD
\n(iii) \u2220 ADC
\n\"Selina
\nSolution:<\/span>
\n\"Selina<\/p>\n

Question 21.<\/span>
\nABCD is a cyclic quadrilateral of a circle with centre o such that AB is a diameter of this circle and the length of the chord CD is equal to the radius of the circle..if AD and BC produced meet at P, show that APB =60\u00b0
\nSolution:<\/span>
\n\"Selina<\/p>\n

Question 22.<\/span>
\nIn the figure, given alongside, CP bisects angle ACB. Show that DP bisects angle ADB.
\n\"Selina
\nSolution:<\/span>
\n\"Selina<\/p>\n

Question 23.<\/span>
\nIn the figure, given below, AD = BC, \u2220 BAC = 30\u00b0 and \u2220 = 70\u00b0 find:
\n(i) \u2220 BCD
\n(ii) \u2220 BCA
\n(iii) \u2220 ABC
\n(iv) \u2220ADC
\n\"Selina
\nSolution:<\/span>
\n\"Selina<\/p>\n

Question 24.
\n<\/span>In the figure given below, AD is a diameter. O is the centre of the circle. AD is parallel to BC and \u2220CBD = 32\u00b0. Find :
\n(i) \u2220OBD
\n(ii) \u2220AOB
\n(iii) \u2220BED (2016)
\nSolution:<\/span>
\n<\/span>i. AD is parallel to BC, i.e., OD is parallel to BC and BD is transversal.
\n\"Selina<\/p>\n

\"Selina<\/p>\n

\"Selina<\/p>\n

Question 25.
\n<\/span>In the figure given, O is the centre of the circle.\u00a0\u2220DAE = 70\u00b0. Find giving suitable reasons, the measure of
\ni. \u2220BCD
\nii. \u2220BOD
\niii.\u00a0\u2220OBD
\n\"Selina
\nSolution:<\/span>
\n<\/span>\u2220DAE and\u00a0\u2220DAB are linear pair
\nSo,
\n\u2220DAE +\u00a0\u2220DAB = 180\u00b0
\n\u2234\u2220DAB = 110\u00b0<\/p>\n

Also,
\n\u2220BCD +\u00a0\u2220DAB = 180\u00b0\u2026\u2026Opp. Angles of cyclic quadrilateral BADC
\n\u2234\u2220BCD = 70\u00b0
\n\u2220BCD = \\(\\frac { 1 }{ 2 }\\) \u2220BOD\u2026angles subtended by an arc on the centre and on the circle
\n\u2234\u2220BOD = 140\u00b0<\/p>\n

In\u00a0\u0394BOD,
\nOB = OD\u2026\u2026radii of same circle
\nSo,
\n\u2220OBD =\u2220ODB\u2026\u2026isosceles triangle theorem
\n\u2220OBD +\u00a0\u2220ODB +\u00a0\u2220BOD = 180\u00b0\u2026\u2026sum of angles of triangle
\n2\u2220OBD = 40\u00b0
\n\u2220OBD = 20\u00b0<\/p>\n

More Resources for Selina Concise Class 10 ICSE Solutions<\/strong><\/p>\n