Question

If tangents PA and PB from a point P to a circle with centre O are drawn so that ∠APB = 80° then ∠POA = ?

Options

• 40°

• 50°

• 80°

• 60°

Answer 1

50°

Explanation:

OP bisects the angle between the equal tangents, so ∠OPA = `(80^circ)/2` = 40°. 

In triangle POA, OA ⟂ PA so ∠OAP = 90°.

Thus ∠POA = 90° – 40° = 50°.