Question

In the given figure, 4 × CP = PD = 12 cm and AP = 9 cm, find BP.

Answer 1

Given

4 × CP = PD = 12 cm

AP = 9 cm

Find BP.

Step 1: Find CP and PD

Since 4 × CP = 12

CP = 12 ÷ 4

CP = 3 cm

Given PD = 12 cm

So:

CP = 3 cm

PD = 12 cm

Step 2: Use the Intersecting Chords Theorem

For two intersecting chords inside a circle:

AP × BP = CP × DP

Substitute the values:

AP × BP = 3 × 12

9 × BP = 36

Step 3: Solve for BP

BP = 36 ÷ 9

BP = 4 cm