Q. 65.0( 2 Votes )

PQ is a tangent t

Answer :


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, ∆POQ is right-angled at OPQ (i.e., OPQ = 90°).


POQ is an isosceles triangle


POQ = OQP


By property 2,


POQ + OQP + QPO = 180°


POQ + OQP = 180° - QPO


POQ + OQP = 180° - 90°


POQ + OQP = 180° - 90°


POQ + OQP = 90°


OQP + OQP = 90° [∵∠POQ = OQP]


2OQP = 90°


OQP = 45°


Hence, OQP = 45°

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