From a point P wh

Given: radius = 5 cm

To find: area of the quadrilateral PQOR

Explanation:

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

As Area of right-angled triangle

[Using 1 and 2]