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In ∆Abc, Ray Ad Bisects ∠A and Intersects Bc in D. If Bc = A, Ac = B and Ac = C, Prove that D C = a B B + C - Mathematics

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Question

In ∆ABC, ray AD bisects ∠A and intersects BC in D. If BC = a, AC = b and AC = c, prove that \[DC = \frac{ab}{b + c}\]

Sum

Solution

Since BC = CD + BD

`⇒ CD =BC -BD`

`CD = a - (ac)/(b+c)`

`= (ab)/(b+c)`

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Chapter 7: Triangles - Exercise 7.8 [Page 127]

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RD Sharma Mathematics [English] Class 10
Chapter 7 Triangles
Exercise 7.8 | Q 25.2 | Page 127

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