# 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 isA. 60cm2B. 65cm2C. 30cm2D. 32.5cm2

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 

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] 

Area of quadrilateral PQRS, A = area of POQ + area of POR   [Using 1 and 2]

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