**Selina Concise Mathematics Class 10 ICSE Solutions Tangents and Intersecting Chords**

APlusTopper.com provides step by step solutions for Selina Concise ICSE Solutions for Class 10 Mathematics Chapter 18 Tangents and Intersecting Chords. You can download the Selina Concise Mathematics ICSE Solutions for Class 10 with Free PDF download option. Selina Publishers Concise Mathematics for Class 10 ICSE Solutions all questions are solved and explained by expert mathematic teachers as per ICSE board guidelines.

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**Selina ICSE Solutions for Class 10 Maths Chapter 18 Tangents and Intersecting Chords**

**Exercise 18(A)**

**Question 1.**

The radius of a circle is 8 cm. Calculate the length of a tangent drawn to this circle from a point at a distance of 10 cm from its centre?

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**Question 2.**

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**Question 3.**

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**Question 4.**

Two circles touch each other internally. Show that the tangents drawn to the two circles from any point on the common tangent are equal in length.

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**Question 5.**

Two circles of radii 5 cm and 3 cm are concentric. Calculate the length of a chord of the outer circle which touches the inner.

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**Question 6.**

Three circles touch each other externally. A triangle is formed when the centers of these circles are joined together. Find the radii of the circles, if the sides of the triangle formed are 6 cm, 8 cm and 9 cm.

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**Question 7.**

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**Question 8.**

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**Question 9.**

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**Question 10.**

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**Question 11.**

Radii of two circles are 6.3 cm and 3.6 cm. State the distance between their centers if –

i) they touch each other externally.

ii) they touch each other internally.

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**Question 12.**

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**Question 13.**

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**Question 14.**

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**Question 15.**

Two parallel tangents of a circle meet a third tangent at point P and Q. Prove that PQ subtends a right angle at the centre.

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**Question 16.**

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**Question 17.**

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**Question 18.**

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**Question 19.**

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**Question 20.**

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**Question 21.**

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**Question 22.**

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**Question 23.**

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**Exercise 18(B)**

**Question 1.**

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**Question 2.**

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**Question 3.**

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**Question 4.**

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**Question 5.**

AB is diameter and AC is a chord of a circle with centre O such that angle BAC=30ΒΊ. The tangent to the circle at C intersects AB produced in D. Show that BC = BD.

**Solution:**

**Question 6.**

Tangent at P to the circumcircle of triangle PQR is drawn. If this tangent is parallel to side QR, show that triangle PQR is isosceles.

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**Question 7.**

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**Question 8.**

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**Question 9.**

In a cyclic quadrilateral ABCD, the diagonal AC bisects the angle BCD. Prove that the diagonal BD is parallel to the tangent to the circle at point A.

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**Question 10.**

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**Question 11.**

Two circles intersect each other at point A and B. A straight line PAQ cuts the circle at P and Q. If the tangents at P and Q intersect at point T; show that the points P, B, Q and T are concyclic.

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**Question 12.**

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**Question 13.**

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**Question 14.**

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**Question 15.**

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**Question 16.**

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**Exercise 18(C)**

**Question 1.**

Prove that of any two chord of a circle, the greater chord is nearer to the centre.

**Solution:**

**Question 2.**

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**Question 3.**

Two circles with centers A and B, and radii 5 cm and 3 cm, touch each other internally. If the perpendicular bisector of the segment AB meets the bigger circle in P and Q; find the length of PQ.

**Solution:**

**Question 4.**

Two chords AB and AC of a circle are equal. Prove that the centre of the circle, lies on the bisector of the angle BAC.

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**Question 5.**

The diameter and a chord of circle have a common end-point. If the length of the diameter is 20 cm and the length of the chord is 12 cm, how far is the chord from the centre of the circle?

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**Question 6.**

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**Question 7.**

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**Question 8.**

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**Question 9.**

Show that the circle drawn on any one of the equal sides of an isosceles triangle as diameter bisects the base.

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**Question 10.**

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**Question 11.**

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**Question 12.**

Prove that the perimeter of a right triangle is equal to the sum of the diameter of its incircle and twice the diameter of its circumcircle.

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**Question 13.**

P is the midpoint of an arc APB of a circle. Prove that the tangent drawn at P will be parallel to the chord AB.

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**Question 14.**

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**Question 15.**

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**Question 16.**

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**Question 17.**

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**Question 18.**

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**Question 19.**

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**Question 20.**

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**Question 21.**

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**Question 22.**

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**Question 23.**

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**Question 24.**

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**Question 25.**

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**Question 26.**

AB is a line segment and M is its midpoint. Three semicircles are drawn with AM, MB and AB as diameters on the same side of the line AB. A circle with radius r unit is drawn so that it touches all the three semicircles. Show that: AB = 6 x r

**Solution:**

**Question 27.**

TA and TB are tangents to a circle with centre O from an external point T. OT intersects the circle at point P. Prove that AP bisects the angle TAB.

**Solution:**

**Question 28.**

Two circles intersect in points P and Q. A secant passing through P intersects the circle in A and B respectively. Tangents to the circles at A and B intersect at T. Prove that A, Q, B and T lie on a circle.

**Solution:**

**Question 29.**

Prove that any four vertices of a regular pentagon are concyclic (lie on the same circle)

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**Question 30.**

Chords AB and CD of a circle when extended meet at point X. Given AB = 4 cm, BX = 6 cm and XD = 5 cm. Calculate the length of CD.

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**Question 31.**

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**Question 32.**

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**Question 33.**

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**Question 34.**

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**Question 35.**

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**Question 36.**

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**Question 37.**

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**Question 38.**

In two concentric circles prove that all chords of the outer circle, which touch the inner circle, are of equal length.

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**Question 39.**

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**Question 40.**

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**Question 41.**

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**Question 42.**

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**Question 43.**

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**More Resources for Selina Concise Class 10 ICSE Solutions**

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