**Selina ICSE Solutions for Class 10 Maths – Constructions (Circles)**

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**Selina ICSE Solutions for Class 10 Maths Chapter 19 Constructions (Circles)**

**Exercise 19**

**Question 1.**

Draw a circle of radius 3 cm. Mark a point P at a distance of 5 cm from the centre of the circle drawn. Draw two tangents PA and PB to the given circle and measure the length of each tangent.

**Solution:**

**Question 2.**

Draw a circle of diameter of 9 cm. Mark a point at a distance of 7.5 cm from the centre of the circle. Draw tangents to the given circle from this exterior point. Measure the length of each tangent.

**Solution:**

**Question 3.**

Draw a circle of radius 5 cm. Draw two tangents to this circle so that the angle between the tangents is 45º.

**Solution:**

**Question 4.**

Draw a circle of radius 4.5 cm. Draw two tangents to this circle so that the angle between the tangents is 60º.

**Solution:**

**Question 5.**

Using ruler and compasses only, draw an equilateral triangle of side 4.5 cm and draw its circumscribed circle. Measure the radius of the circle.

**Solution:**

**Question 6.**

**Solution:**

**Question 7.**

Using ruler and compasses only, draw an equilateral triangle of side 5 cm. Draw its inscribed circle. Measure the radius of the circle.

**Solution:**

**Question 8.**

**Solution:**

**Question 9.**

**Solution:**

**Question 10.**

Perpendicular bisectors of the sides AB and AC of a triangle ABC meet at O.

(i) What do you call the point O?

(ii) What is the relation between the distances OA, OB and OC?

(iii) Does the perpendicular bisector of BC pass through O?

**Solution:**

**Question 11.**

The bisectors of angles A and B of a scalene triangle ABC meet at O.

i) What is the point O called?

ii) OR and OQ are drawn perpendiculars to AB and CA respectively. What is the relation between OR and OQ?

iii) What is the relation between angle ACO and angle BCO?

**Solution:**

**Question 12.**

i) Using ruler and compasses only, construct a triangle ABC in which AB = 8 cm, BC = 6 cm and CA = 5 cm.

ii) Find its incentre and mark it I.

iii) With I as centre, draw a circle which will cut off 2 cm chords from each side of the triangle.

**Solution:**

**Question 13.**

Construct an equilateral triangle ABC with side 6 cm. Draw a circle circumscribing the triangle ABC.

**Solution:**

**Question 14.**

Construct a circle, inscribing an equilateral triangle with side 5.6 cm.

**Solution:**

**Question 15.**

Draw a circle circumscribing a regular hexagon of side 5 cm.

**Solution:**

**Question 16.**

Draw an inscribing circle of a regular hexagon of side 5.8 cm.

**Solution:**

**Question 17.**

Construct a regular hexagon of side 4 cm. Construct a circle circumscribing the hexagon.

**Solution:**

**Question 18.**

Draw a circle of radius 3.5 cm. Mark a point P outside the circle at a distance of 6 cm from the centre. Construct two tangents from P to the given circle. Measure and write down the length of one tangent.

**Solution:**

**Question 19.**

Construct a triangle ABC in which base BC = 5.5 cm, AB = 6 cm and m∠ABC =120˚.

i. Construct a circle circumscribing the triangle ABC.

ii. Draw a cyclic quadrilateral ABCD so that D is equidistant from B and C.

**Solution:**

**Question 20.**

Using a ruler and compasses only :

(i) Construct a triangle ABC with the following data: AB = 3.5 cm, BC = 6 cm and ∠ABC = 120°.

(ii) In the same diagram, draw a circle with BC as diameter. Find a point P on the circumference of the circle which is equidistant from AB and BC.

(iii) Measure ∠BCP.

**Solution:**

**Question 21.**

Construct a ∆ABC with BC = 6.5 cm, AB = 5.5 cm, AC = 5 cm. Construct the incircle of the triangle. Measure and record the radius of the incircle.

**Solution:**

**Question 22.**

Construct a triangle ABC with AB = 5.5 cm, AC = 6 cm and ∠BAC = 105°. Hence :

(i) Construct the locus of points equidistant from BA and BC.

(ii) Construct the locus of points equidistant from B and C.

(iii) Mark the point which satisfies the above two loci as P. Measure and write the length of PC.

**Solution:**