In triangle ABC, AD is the bisector of ÐA and intersects BC at D. If BC = a, AC = b AB = c then BD is equal to:
Show answer & explanation
Correct answer: D
Explanation
The correct answer is Option 4 i.e. .
Let BD = x.
Then DC = a − x.
By Angle Bisector Theorem:
x / (a − x) = c / b
Cross-multiply:
bx = c(a − x)
bx = ca − cx
bx + cx = ca
x(b + c) = ca
x = ac / (b + c)