# Draw a circle of radius 3 cm. Take two points P and Q on one of its extended diameter each at a distance of 7 cm from its centre. Draw tangents to the circle from these two points P and Q

**Solution:**

Steps of construction:

- Draw a circle with O as centre and radius is 3 cm.
- Draw a diameter of it extend both the sides and take points P, Q on the diameter such that OP = OQ = 7 cm.
- Draw the perpendicular bisectors of OP and OQ to intersect OP and OQ at M and N respectively.
- With M as centre and OM as radius draw a circle to cut the given circle at A and C. With N as the centre and ON as radius draw a circle to cut the given circle at B and D.
- Join PA, PC, QB, QD.

PA, PC and QB, QD are the required tangents from P and Q respectively.

Proof:

∠PAO = ∠QBO =-90° (Angle in a semi-circle)

∴ PA ⊥ AO, QB ⊥ BO

Since OA and OB are the radii of the given circle, PA and QB are its tangents at A and B respectively.

In right angle triangle PAO and QBO

OP = OQ = 7cm (By construction)

OA = OB = 3cm (radius of the given circle)

PA² = (OP)² - (OA)²

= (7)² - (3)²

= 49 - 9

= 40

PA = √40

= 6.3 (approx)

And

QB² = (OQ)² - (OB)²

= (7)² - (3)²

= 49 - 9

= 40

QB = √40

= 6.3 (approx)

**Video Solution:**

## Draw a circle of radius 3 cm. Take two points P and Q on one of its extended diameter each at a distance of 7 cm from its centre. Draw tangents to the circle from these two points P and Q

### NCERT Solutions Class 10 Maths - Chapter 11 Exercise 11.2 Question 3:

Draw a circle of radius 3 cm. Take two points P and Q on one of its extended diameter each at a distance of 7 cm from its centre. Draw tangents to the circle from these two points P and Q

PA and QB are the required tangents of 6.3 cm length each constructed at a distance of 7cm of a circle of radius 3 cm