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

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प्रश्न

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

योग

उत्तर

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

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अध्याय 17: Circles - Exercise 17 (C) [पृष्ठ २६७]

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सेलिना Mathematics [English] Class 10 ICSE
अध्याय 17 Circles
Exercise 17 (C) | Q 22 | पृष्ठ २६७

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