> Solution We have XY || AC (Given) So, ∠ BXY = ∠ A and ∠ BYX = ∠ C (Corresponding angles) Therefore, △ ABC ∼ △ XBY (AA similarity criterion) So, ar (ABC)/ar (XBY) = \((AB/XB)^2\) Also, Ar(△ABC)=2Ar(△XBY) So, Ar(△ABC)Ar(△XBY)=21 (2) Therefore, (ABXB)2= 21 , i.e., ABXB = √21 XBAB = 1√2 or, 1 – XBAB = 1 – 1√2 or, AB−XBAB = (√2–1)/√2, i.e., AXAB =(2–√2)/2 Suggest Corrections |