Question

In the figure, given below, CP bisects angle ACB. Show that DP bisects angle ADB.

Answer 1

Given – In the figure, CP is the bisector of ∠ABC

To prove – DP is the bisector of ∠ADB

Proof – Since CP is the bisector of ∠ACB

∴ ∠ACP = ∠BCP

But ∠ACP = ∠ADP   ...[Angle in the same segment of the circle]

And ∠BCP = ∠BDP

But ∠ACP = ∠BCP

∴ ∠ADP = ∠BDP   

∴ DP is the bisector of ∠ADB