Q. 93.6( 10 Votes )

In a triangle ABC, X

Answer :

Given: ABC is a triangle with XY || AC divides the triangle into two parts equal in areas.
To find:
Proof:
ar ΔBXY = ar trap. XYCA (Given) ∴ ar ΔBXY = ar ΔABC
In ΔBXY andBAC,
∠BXY = ∠BAC (Corresponding angles)
∠BYX = ∠BCA (Corresponding angles)
ΔBXY ∼ ΔBAC (AA similarity)
= (Areas of similar triangle)
=
=
∴ AB – BX = √ 2 BX – BX
∴ AX = (√ 2 – 1)BX
= =.

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