Q4 of 42 Page 214

In Δ ABC, XY || AC and XY divides the triangle into two parts of equal area. Find the ratio of

Given, XY || AC


Need to find the ratio of AX:XB



⇒ ∠1 = ∠3 and ∠2 = ∠4 [corresponding angles]


⇒ Δ BXY ∼ Δ BAC


⇒ ……….eq(1)


Also, we are given that


⇒ ar(Δ BXY) = ar(Δ BAC)


⇒


From (1) and (2)


⇒


⇒


⇒ Now, -1 =


⇒ =


∴ AX:XB = √2 -1 : 1


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