Question

For a circle with centre O, two tangents PA and PB form an angle of 80° from

an external point P. find m POA.​

Answer 1

Given :- For a circle with centre O, two tangents PA and PB form an angle of 80° from an external point P. find m POA. ?

Solution :-

given that,

→ ∠APB = 80° .

→ OA = OB = radius .

we know that,

• Radius is perpendicular to the tangent at the point of contact .
• OP will be angle bisector of ∠P .

so,

→ ∠OAP = 90°

→ ∠OPA = 80/2 = 40° .

now, in right ∆OAP ,

→ ∠OAP + ∠OPA + ∠POA = 180° (By angle sum Property.)

→ 90° + 40° + ∠POA = 180°

→ 130° + ∠POA = 180°

→ ∠POA = 180° - 130°

→ ∠POA = 50° (Ans.)

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