Q. 235.0( 1 Vote )

In Fig. 10.85, if

Answer :

Given:


RPQ = 60°


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


OP = OQ [ radius of circle]


OPQ = OQP = 30°


Now by property 2,


OPQ + OQP + POQ = 180°


30° + 30° + POQ = 180°


60° + POQ = 180°


POQ = 180° - 60°


POQ = 120°


Hence, POQ = 120°

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