In the following figure, ∠AXY = ∠AYX. If BX/AX = CY/AY, show that triangle ABC is isosceles.

Solution:

According to the given question,

   

So,

   

[Sides opposite to equal angles are equal.]

Also, from BPT we have

   

Thus,

   

So,

   

Therefore,

   

is an isosceles triangle.