Question

In the following figure, ΔABC is circumscribing a circle. Find the length of BC.

Answer 1

According to the theorem of tangents, tangents drawn from an external point to a circle are equal in length. 

1. Find AQ:

Tangents from point A are AR and AQ.

AQ = AR = 4 cm 

2. Find QC:

The total length of AC is given as 11 cm. 

QC = AC – AQ 

QC = 11 cm – 4 cm

QC = 7 cm 

3. Find BP and CP:

Tangents from point B are BR and BP, so BP = BR = 3 cm.

Tangents from point C are QC and CP, so CP = QC = 7 cm. 

4. Calculate BC: 

BC = BP + CP 

BC = 3 cm + 7 cm

BC = 10 cm