Q. 344.3( 3 Votes )

In Fig. 10.96, if

Answer :

Given:


TQP = 60°


Property 1: If two tangents are drawn to a circle from one external point, then their tangent segments (lines joining the external point and the points of tangency on circle) are equal.


Property 2: The tangent at a point on a circle is at right angles to the radius obtained by joining center and the point of tangency.


By property 1,


TP = TQ (tangent from T)


TPQ = TQP = 60°


By property 2, ∆OPT is right-angled at OPT (i.e., OPT = 90°) and OQT is right-angled at OQT (i.e., OQT = 90°).


Now,


OPQ = OPT TPQ


OPQ = 90° 60°


OPQ = 30°


Hence, OPQ = 30°

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