Question

If tangents PA and PB from a point P to a circle with centre O are inclined to each other an angle of 80, then ∠POA is equal to

(A) 50 (B) 60

(C) 70 (D) 80

Answer 1

Given : tangents PA and PB from a point P to a circle with centre O, are inclined to each other at an angle of 80°,

To Find : ∠POA

Solution:

PA & PB are tangent and O is tangent

=> ∠OAP = ∠ OBP = 90°

PA and PB are inclined to each other at 80°

=> ∠APB = 80°

in Quadrilateral OAPB

∠AOB + ∠OAP + ∠APB + ∠ OBP = 360°

=> ∠APB + 90° + 80° + 90° = 360°

=> ∠APB = 100°

∠POA = ∠POB = (1/2) ∠APB

=> ∠POA = (1/2) 100°

=> ∠POA = 50°

option (A) is correct