Question

What information guarantees that xy is parallel to ac?

Answer 1

In triangle ABC and Triangle XBY,

Angle ABC = Angle XBY

Angle ACB = Angle XYB

Triangle ABC - Triangle  XBY

Triangle ABC - Triangle XBY

Now, we know that in similar triangles Ratio of Area of the triangle is equal to the ratio of the square of corresponding sides:

Area of triangle ABC/ Area of triangle XBY = (AB/XB)²