Question

In the given circle with centre O, AM = MB = 12 cm and MC = 6 cm. Find the radius of the circle.

Answer 1

Step 1:

Let the radius of the circle be r

OC is a radius, so OC = r

OM = OC – MC

OM = r – 6

Step 2:

In right-angled triangle OMA, OA is the hypotenuse.

OA² = OM² + AM²

r² = (r – 6)² + 12²

Step 3:

r² = r² – 12r + 36 + 144

0 = –12r + 180

12r = 180

`r = 180/12`

r = 15

The radius of the circle is 15 cm.