# 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 angle POA is equal to.

Important NCERT Questions

Circles

NCERT Books for Session 2022-2023

CBSE Board and UP Board Others state Board

EXERCISE 10.2

Page No:213

Questions No:3

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Given: PA and PB are two tangents of the circle.

We know that the radius is perpendicular to tangent. Therefore, OA ⊥PA and OB PB.

⇒ ∠OBP = 90° and ∠OAP = 90°

In quadrilaterral AOBP, ∠OAP + ∠APB + ∠PBO + ∠BOA = 360°

⇒ 90° + 80° + 90° + ∠BOA = 360°

⇒ ∠BOA = 360° – 260° = 100°

In ΔOPB and ΔOPA,

AP = BP [Tangents drawn from same external point]

OA = OB [Radii]

OP = OP [Common]

Therefore, ΔOPB ≅ ΔOPA [SSS Congruency rule]

Hence, ∠POB = ∠POA

∠POA = 1/2 ∠AOB = 1/2(100°) = 50°. Hence, the option (A) is correct.

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