# Draw a circle of radius 6 cm. From a point 10 cm away from its centre, construct the pair of tangents to the circle and measure their lengths

**Solution:**

Steps of construction:

- Take a point O as the centre and 6 cm radius. Draw a circle.
- Take a point P in such a manner that OP = 10cm
- With O and P as centres and radius more than half of OP draw arcs above and below OP to intersect at X and Y.
- Draw line segment XY to intersect OP at M.
- With M as the centre and OM as radius draw a circle to intersect the given circle at Q and R.
- Join PQ and PR. PQ and PR are the tangents, where PQ and PR = 8cm.

Proof:

∠PQO = 90 ⇒ PQ ⊥ OQ (Angle in a semicircle)

In right ΔPQO,

OP = 10 cm, OQ = 6cm (radius)

PQ² = OP² - OQ²

= (10)² - (6)²

= 100 - 36

= 64

PQ = √64

= 8 cm

Similarly, PR = 8 cm.

**Video Solution:**

## Draw a circle of radius 6 cm. From a point 10 cm away from its centre, construct the pair of tangents to the circle and measure their lengths

### NCERT Solutions Class 10 Maths - Chapter 11 Exercise 11.2 Question 1:

Draw a circle of radius 6 cm. From a point 10 cm away from its centre, construct the pair of tangents to the circle and measure their lengths

PQ and PR are the required tangents of 8 cm length each constructed from a point 10 cm away from the centre of a circle of radius 6 cm