Question

In the given figure, the diameter CD of a circle with centre O is perpendicular to chord AB. If AB = 12 cm and CE = 3 cm, calculate the radius of the circle.

Answer 1

From the figure we know that CD is the diameter of the circle with centre O which is perpendicular to chord AB.

Draw the line OA.

It is given that AB = 12cm and CE = 3cm

Consider OA = OC = r cm

It can be written as

OE = (r – 3) cm

Perpendicular from the centre of a circle to a chord bisects the chord

We know that

AE = ½ × AB

By substituting the values

AE = ½ × 12

So we get

AE = 6 cm

Consider △ OEA

By using the Pythagoras theorem

OA² = OE² + AE²

By substituting the values

r² = (r – 3)² + 6²

So we get

r² = r² – 6r + 9 + 36

On further calculation

r² – r² + 6r = 45

So we get

6r = 45

By division

r = 45/6

r = 7.5 cm

Therefore, the radius of the circle is 7.5 cm.