Q. 44.2( 5 Votes )

Two tangents TP and TQ are drawn from an external point T to a circle with center O as shown in Fig. 10.73. If they are inclined to each other at an angle of 100°, then what is the value of POQ?


Answer :

Given:


QTP = 100°


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 quadrilateral = 360°.


By property 1,


OPT = 90° and OQT = 90°


And,


By property 2,


QTP + OPT + OQT + POQ = 360°


POQ = 360° QTP + OPT + OQT


POQ = 360° – 100° + 90° + 90°


POQ = 360° – 280°


POQ = 80°


Hence, POQ = 80°


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