Q18 of 35 Page 11

In the given figure, two radii OP and OQ of a circle are mutually perpendicular. What is the degree measure of the angle between tangents drawn to the circle at P and Q?

a) we have to find ∠PTQ which is the angle between the tangents TP and TQ


∠OPT = ∠OQT = 90° …radius is perpendicular to tangent at point of contact


∠POQ = 90° …given


Consider quadrilateral POQT


⇒ ∠OPT + ∠OQT + ∠POQ + ∠PTQ = 360° …sum of angles of quadrilateral


⇒ 90° + 90° + 90° + ∠PTQ = 360°


⇒ 270° + ∠PTQ = 360°


⇒ ∠PTQ = 90°


Hence angle between tangents is 90°


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