Question

The length of a chord of a bigger circle concentric with a circle of radius 3 cm is 8 cm. If the chord is a tangent to the smaller circle, then find the radius of the bigger circle.

Answer 1

Given: Two concentric circles with common center O; radius of smaller circle OP = 3 cm. A chord AB of the larger circle is tangent to the smaller circle and AB = 8 cm.

Step-wise calculation:

1. Tangent at P implies OP ⟂ AB.

So OP meets AB at its midpoint P.

Hence AP = PB

= `1/2` × AB

= 4 cm

2. In right triangle OAP, by Pythagoras:

OA² = OP² + AP² 

= 3² + 4²

= 9 + 16

= 25

3. Therefore OA = `sqrt(25)` = 5 cm.

The radius of the bigger circle is 5 cm.