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 Z POA is equal to​

Answer 1

∠POA= ∠POB = 50°

Explanation:

The diagram of the given question has been drawn in the attachment.

From the diagram

Δ PAO is congruent to Δ PBO.

as PO is common in Δ

∠ PAO = ∠PBO = 90°

PA =PB [ tangent from an external point]

⇒∠POA= ∠POB

Also, ∠APB+ ∠AOB = 180°

⇒ 80° + ∠AOB = 180°

⇒∠AOB = 100°

⇒ ∠POA= ∠POB = 50°