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In the Figure, Given Alongside, Cp Bisects Angle Acb. Show that Dp Bisects Angle Adb. - Mathematics

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Question

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

Solution

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

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APPEARS IN

 Selina Solution for Concise Mathematics for Class 10 ICSE (2020 (Latest))
Chapter 17: Circles
Exercise 17(C) | Q: 22 | Page no. 267
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In the Figure, Given Alongside, Cp Bisects Angle Acb. Show that Dp Bisects Angle Adb. Concept: Arc and Chord Properties - Angles in the Same Segment of a Circle Are Equal (Without Proof).
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