In the figure, given alongside, CP bisects angle ACB. Show that DP bisects angle ADB.
Exercise 17 (C) | Q 22 | Page 267
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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
And ∠BCP = ∠BDP
But ∠ACP = ∠BCP
∴ ∠ADP = ∠BDP
∴ DP is the bisector of ∠ADB
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
And ∠BCP = ∠BDP
But ∠ACP = ∠BCP
∴ ∠ADP = ∠BDP
∴ DP is the bisector of ∠ADB
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