# Circle

## Exercise 10.2 Part 2

Question: 3 - If tangents PA and PB from a point P to a circle with centre O are inclined to each other at angle of 80°, then ∠POA is equal to

- 50°
- 60°
- 70°
- 80°

**Answer:** (a) 50°

**Explanation:** Here; `∠APB = 80°`

`∠OPA = ½ xx ∠APB`

`= ½ xx 80^o = 40^o`

In ΔPOA;

`∠OPA + ∠OAP + ∠POA = 180°`

Or, `40° + 90° + ∠POA = 180°`

Or, `∠POA = 180° - 130° = 50°`

Question: 4 - Prove that the tangents drawn at the ends of a diameter are parallel.

**Answer:** Construction: Draw a circle with centre O. Draw a diameter AB. Draw tangents MN and OP which respectively touch A and B.

**To Prove:** MN || OP

`∠MAB = ∠PBA = 90°` (since radius is perpendicular to tangent

Since alternate angles are equal

Hence; MN || OP proved