Question

Two chords AB and CD of a circle intersect each other at P outside the circle. If AB 5 cm, BP 3 cm and PD 2 cm, find CD.

Answer 1

Answer:

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=

2.5

9.75

So we get

x=3.9cm

Therefore, CD=3.9cm.