Question

In the given figure, XY║AC and XY divides ∆ABC into two regions, equal in area. Show that AX/AB = (2− √2)/2.

Answer 1

In ∆ ABC and ∆BXY, we have: 

∠B = ∠B

∠BXY = ∠BAC (corresponding angles) 

Thus, ∆ABC − ∆BXY (AA creterion)

Also, ar(∆ABC)/ar(∆BXY) = 2/1 {∴ ar (∆BXY) = ar(trapezium AXYV)} … (ii) 

From (i)and (ii), we have: