Question

In triangle ABC, ray AD bisects angle A and intersects BC in D. If BC = a, AC = b and AB =c, prove that BD = ac/(b+c)

Answer 1

hope this helps you .............

Answer 2

Answer:

The proof is explained below.

Step-by-step explanation:

Given that in triangle ABC, ray AD bisects angle A and intersects BC in D. If BC = a, AC = b and AB =c,

we have to prove that $BD=\frac{ac}{b+c}$

Since AB bisects ∠A

$\frac{AC}{AB}=\frac{DC}{BD}$

$\frac{b}{c}=\frac{DC}{BD}$

$\frac{b}{c}+1=\frac{DC}{BD}+1$

$\frac{b+c}{c}=\frac{BC}{BD}=\frac{a}{BD}$

$BD=\frac{ac}{b+c}$

Hence proved