Class 10 Maths

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:

- 7 cm
- 12 cm
- 15 cm
- 24.5 cm

**Answer:**(a) 7 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

- 60°
- 70°
- 80°
- 90°

**Answer:** (b) 70°

**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°`

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