# 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

1. 50°
2. 60°
3. 70°
4. 80°

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