Question

In the adjoining figure, bisectors of ∠B and ∠C of ∆ABC intersect each other in point X. Line AX intersects side BC in point Y. 

AB = 5, AC = 4, BC = 6, then find AX/XY.

Answer 1

Let the value of BY be x. BC = BY + YC [B – Y – C] 

∴ 6 = x + YC 

∴ YC = 6 – x 

in ∆BAY, ray BX bisects ∠B. [Given] 

∴ AB/BY = AX/XY  (i) [Property of angle bisector of a triangle]

Also, in ∆CAY, ray CX bisects ∠C. [Given]