Question

In ∆ABC, ray AD bisects ∠A and intersects BC in D. If BC = a, AC = b and AC = c, prove that

(i) $\mathrm{BD}=\frac{ac}{b+c}$
(ii) $\mathrm{DC}=\frac{ab}{b+c}$

Answer 1

Given: In ray AD bisects angle A and intersects BC in D, If and

To Prove:

(i)

(ii)

(i) The corresponding figure is as follows

Proof: In triangle ABC, AD is the bisector of

Therefore

Substitute and we get,

By cross multiplication we get.

We proved that

(ii) Since BC = CD + BD