Q. 44.8( 6 Votes )

From a point P which is at a distance of 13 cm from the center 0 of a circle of radius 5 cm, the pair of tangents PQ and PR to the circle is drawn. Then, the area of the quadrilateral PQOR is
A. 60cm2

B. 65cm2

C. 30cm2

D. 32.5cm2

Answer :

Let us draw a circle of radius 5 cm having center O. P is a point at a distance of 13 cm from O. A pair of tangents PQ and PR are drawn.


Also, OQ = OR = radius = 5cm [1]


And OP = 13 cm



As OQ PQ and OR PR [ As tangent to at any point on the circle is perpendicular to the radius through point of contact]


POQ and POR are right-angled triangles.


In PQO By Pythagoras Theorem [ i.e. (base)2+ (perpendicular)2= (hypotenuse)2 ]


(PQ)2 + (OQ)2= (OP)2


(PQ)2 + (5)2 = (13)2


(PQ)2 + 25 = 169


(PQ)2 = 144


PQ = 12 cm


And


PQ = PR = 12 cm [ tangents through an external point to a circle are equal] [2]


Area of quadrilateral PQRS, A = area of POQ + area of POR




[Using 1 and 2]

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