Question

In given figure, chords AB and CD of a circle
intersect at P. If AB = 5 cm, PB = 3 cm and PD
= 4 cm, then find the length of CD.
​

Answer 1

CD = 2 cm

Step-by-step explanation:

Here chords AB and CD of a circle intersect at P.

AB = 5 cm, PB = 3 cm and PD = 4 cm, CD = ?

Let us assume CD = x

We know that if chords AB and CD intersect externally at point P then

$PB\times PA=PD \times PC$

$3 \times (5+3) = 4\times (x+4)$

24 = 4x+16

4x = 24-16

4x = 8

x = 2 cm

Therefore, CD = 2 cm.

Answer 2

Step-by-step explanation:

AP x PB = DP x PC

3 x 2 = 4 x PC

6/4 = PC

1.5 = PC

PC + PD = DC

1.5 + 4 = DC

5.5 cm = DC