1. If O is the centre of a circle of radius 5 cm. At a distance of 13 cm from O, a point P is taken. From this point, two tangents PQ and PR are drawn to the circle. Then , the area of quadrilateral PQOR is
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- By: anil on 05 May 2019 01.49 amGiven : OQ = 5 cm and OP = 13 cm To find : ar(PQOR) = ? Solution : The radius intersects the tangent at the circumference of the circle at right angle. => $$angle OQP=90^circ$$ In $$ riangle$$ PQO => $$(PQ)^2=(OP)^2-(OQ)^2$$ => $$(PQ)^2=(13)^2-(5)^2$$ => $$(PQ)^2=169-25=144$$ => $$PQ=sqrt{144}=12$$ cm Similarly, PR = 12 cm $$ herefore$$ Area of quad(PQOR) = $$ar( riangle POQ)+ar( riangle POR)$$ = $$PQ imes OQ$$ = $$12 imes 5=60$$ $$cm^2$$ => Ans - (A)
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