Question

In the following figure, CP and CQ are tangents from an external point C to a circle with centre O. AB is another tangent which touches the circle at R. If CP = 11 cm and BR = 4 cm, find the length of BC.

Hint: Given, CP = 11 cm.

∴ CP = CQ ⇒ CQ = 11cm.

Tangents drawn point B are equal.

∴ BR = BQ ⇒ BQ = 4 cm.

Hence, BC = CQ – BQ = (11 – 4) cm = 7 cm.

Answer 1

Given: CP = 11 cm, BR = 4 cm.

Step-wise calculation:

1. Tangents from the same external point are equal.

So CP = CQ

⇒ CQ = 11 cm

2. Tangents from point B to the circle are equal.

So BR = BQ

⇒ BQ = 4 cm

3. BC = CQ – BQ

= 11 – 4

= 7 cm