# Draw a circle of radius 4 cm. Construct a pair of tangents to it, the angle between which is 60º. Also justify the construction. Measure the distance between the centre of the circle and the point of intersection of tangents

**Solution:**

Steps of construction:

1. Construct a __circle__ with O as centre and 4 cm radius

2. Construct any __diameter__ AOB

3. Construct an angle ∠AOP = 60º where OP is the radius which intersect the circle at the point P

4. Construct PQ __perpendicular__ to OP and BE perpendicular to OB

PQ and BE intersect at the point R

5. RP and RB are the required tangents

6. The measurement of OR is 8 cm

Justification:

PR is the tangent to a circle

∠OPQ = 90º

BR is the tangent to a circle

∠OBR = 90º

So we get

∠POB = 180 - 60 = 120º

In BOPR

∠BRP = 360 - (120 + 90 + 90) = 60º

Therefore, the distance between the centre of the circle and the point of intersection of tangents is 8 cm.

**✦ Try This: **Draw a circle of radius 5 cm. Construct a pair of tangents to it, the angle between which is 30º. Also justify the construction. Measure the distance between the centre of the circle and the point of intersection of tangents.

**☛ Also Check:** NCERT Solutions for Class 10 Maths Chapter 11

**NCERT Exemplar Class 10 Maths Exercise 10.4 Problem 6**

## Draw a circle of radius 4 cm. Construct a pair of tangents to it, the angle between which is 60º. Also justify the construction. Measure the distance between the centre of the circle and the point of intersection of tangents

**Summary:**

A circle of radius 4 cm is drawn. A pair of tangents is constructed where the angle between which is 60º. The measurement of the distance between the centre of the circle and the point of intersection of tangents is 8 cm

**☛ Related Questions:**

- Draw an isosceles triangle ABC in which AB = AC = 6 cm and BC = 5 cm. Construct a triangle PQR simil . . . .
- Draw a triangle ABC in which AB = 5 cm, BC = 6 cm and ∠ABC = 60º . Construct a triangle similar to ∆ . . . .
- Draw a triangle ABC in which AB = 4 cm, BC = 6 cm and AC = 9 cm. Construct a triangle similar to ∆AB . . . .

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