(Q5) In ∆ABC, XY ∥ AC and XY divides the triangle into two parts of equal area. Find the ratio of

AX

XB

Solution :

Given :In ∆ABC, XY ∥ AC.

XY divides ∆ABC into two points of equal area.

In ∆ABC, ∆XBY

∠B = ∠

∠ = ∠X

∠C = ∠

[∵ XY ∥ AC; (∠A, ∠X) and ∠C, ∠Y are the pairs of corresponding angles]

Thus ∆ABC ∼ ∆XBY by A.A.A similarity condition.

[∵ The ratio of areas of two similar triangles is equal to the ratio of squares of their corresponding sides]

[Given, ∆BXY = ∆BAC]

[∴ ∆ABC = 2. ∆XBY]