Question

Let abc be a triangle in which ab = ac and let i be its in-centre. Suppose bc = ab + ai. Find angle bac.

Answer 1

Answer:

90°

Step-by-step explanation:

Let AB = c

BC = a

AC = b

Bisector of ∠BAC meets BC at Point D. ID = r

BC = AB + AI  

∴ a = c + AD - r  

a = c + (c² - (a/2)²)^1/2  -- Here AD will be altitude. So by Pythagorus, AD - r = (c² - (a/2)²)^1/2

Solving above we get , a = 2^1/2 c

By, Pytharorus, AD = a/2

∠BAC = 90° hence ∠BAC = 45°