Question

79. In the given figure, TPT is the tangent of circle.
If Z POA = 140", then 2 APT' will be
IT
(A) 20
(B) 90
(C) 70
(D) 60​

Answer 1

The radius of the circle is OP and OA, so they are same length. This means the ∆ is isosceles, hence the angles OPA and OAP are same.

140+OPA+OAP=180

140+2OPA=180

OPA=20°

We know since TPT' is a tangent, OP perpendicular to TPT' hence angle OPT' is 90°

=> OPT' = OPA+ APT'

90 = 20+ APT'

APT'= 70°

The required angle is 70°.