Question

From a point P which is at a distance of 13 cm from the centre o of a circle of radius 5
cm, the pair of tangents PQ and PR to the circle are drawn. Then find the area of the
quadrilateral PQOR.

​

Answer 1

Answer:

60 cm²

Step-by-step explanation:

Use image given below as reference.

It is known that 2 tangents from the same point to a circle are equal.

∴ PQ = PR

We also know that a radius is perpendicular on a tangent.

Thus, OQ is perpendicular to PQ.

OQ = 5 cm (given as radius)

OP  = 13 cm (given)

Applying Pythagoras' theorem,

OQ² + PQ² = OP²

5² + PQ² = 13²

=> 25 + PQ² = 169

∴ PQ² = 169 - 25 => 144

∴ PQ = √144 => 12 cm

As PQ = PR, PR is also 12 cm.

∴ Area of POQ = bh/2 => 12*5/2 => 30 cm²

∴ Area of POR = bh/2 => 12*5/2 => 30 cm²

Now, area of PQOR = area of POQ + area of POR

=> area of PQOR = (30 + 30) cm²

∴ Area of PQOR = 60 cm²