Question

In the given figure, PA = 3 cm, AB = 5 cm, PC = 4 cm, find CD.

Answer 1

Given

PA = 3 cm

AB = 5 cm

PC = 4 cm

Find CD.

In the figure, two secants from point P intersect the circle:

Secant 1: P → A → B

Secant 2: P → C → D

Step 1: Find PB

PB = PA + AB

PB = 3 + 5

PB = 8 cm

Step 2: Use the External Secant Segment Theorem

For two secants from external point P:

PA × PB = PC × PD

Substitute values:

3 × 8 = 4 × PD

24 = 4PD

Step 3: Find PD

PD = 24 ÷ 4

PD = 6 cm

Step 4: Find CD

On the second secant:

PD = PC + CD

6 = 4 + CD

CD = 6 − 4

CD = 2 cm