Q. 265.0( 1 Vote )

In Fig. 10.88, AP

Answer :

Given:


QPB =50°


Property 1: The tangent at a point on a circle is at right angles to the radius obtained by joining center and the point of tangency.


Property 2: Sum of all angles of a triangle = 180°.


By property 1, ∆OPB is right-angled at OPB (i.e., OPB = 90°).


OPQ = OPB QPB


OPQ = 90° 50° = 40°


And,


OPQ = OQP [ OP = OQ (radius of circle)]


Now by property 2,


OPQ + OQP + POQ = 180°


40° + 40° + POQ = 180°


80° + POQ = 180°


POQ = 180° - 80°


POQ = 100°


Hence, POQ = 100°

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