In fig, the line segment XY is parallel to side AC of △ABC and it divides the triangle into two parts of equal areas. Find the ratio AXAB
We are given that XY || AC.
⇒ ∠1 = ∠3 and ∠2 = ∠4 [ corresponding angles ]
⇒ △BXY ~ △BAC [ AA similarity ]
⇒ ar (△BXY)ar (△BAC)=(BX)2(BA)2 [ By theorem] ..... (i)
Also, we are given that
ar (△ BXY ) = ar (△ BAC ) ⇒ ar(△BXY)ar(△BAC)=(12)12 ....(ii)