Q. 95.0( 3 Votes )

PQ is a tangent d

Answer :

Given:


POR = 120°



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 straight line = 180°.


Property 3: Sum of all angles of a triangle = 180°.


By property 1,


PQO = 90°


By property 2,


POQ + POR = 180°


POQ + 120° = 180°


POQ = 180° - 120°


POQ = 60°


Now by property 3 in ∆OPQ,


POQ + PQO + OPQ = 180°


OPQ = 180° - POQ + PQO


OPQ = 180° - (60° + 90°)


OPQ = 180° - 150°


OPQ = 30°


Hence, OPQ = 30°

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