Circle NCERT Exercise 10.2 solution part one Class Ten Mathematics

# Circle

## Exercise 10.2 Part 1

Question: 1 - From a point Q, the length of the tangent to a circle is 24 cm and the distance of Q from the centre is 25 cm. the radius of the circle is:

1. 7 cm
2. 12 cm
3. 15 cm
4. 24.5 cm

Explanation: Here; PQ = 24 cm, OQ = 25 cm, OP = ?

In ΔOPQ

OQ^2 = OP^2 + PQ^2

Or, OP^2= OQ^2 – PQ^2

= 25^2 – 24^2

= 625 – 576 = 49

Or, OP = 7 cm

Question: 2 - In the given figure; if TP and TQ are two tangents to a circle with centre O so that ∠POQ=110°, then ∠PTQ is equal to

1. 60°
2. 70°
3. 80°
4. 90°

Explanation: Here; ∠OPT = ∠OQT = 90° (Since radius is perpendicular to tangent)

Hence, ∠POQ + ∠PTQ = 180°

Or, 110° + ∠PTQ = 180°

Or, ∠PTQ = 180° - 110°

Or, ∠PTQ = 70°