Question

Two chords AB and CD of a circle intersect each other at P outside the circle. If AB = 6cm, BP = 2cm and PD = 2.5cm, find CD.

Answer 1

It is given that AB and CD of a circle intersect each other at P outside the circle. If AB = 6cm, BP = 2cm and PD = 2.5cm

So we get

AP × BP = CP × DP

From the figure we know that CP = CD + DP

By substituting the values

8 × 2 = (CD + 2.5) × 2.5 cm

Consider x = CD

So we get

8 × 2 = (x + 2.5) × 2.5

On further calculation

16 = 2.5x + 6.25

It can be written as

2.5x = 16 – 6.25

By subtraction

2.5x = 9.75

By division

x = 9.75/2.5

So we get

x = 3.9cm

Therefore, CD = 3.9cm.