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Question

In the figure, XY AC and XY divides the triangular region ABC into two equal areas.

Determine AX : XB.

185962_bd10ac20546d4727b674672747831854.png

A
(31):1
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B
(21):1
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C
(71):1
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D
(111):1
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Solution

The correct option is B (21):1
Ar. AXYC = Ar. BXY
Ar. AXYC +Ar. BXY =2 Ar. BXY
Ar.ABC =2 Ar. BXY
Hence, Ar.ABCAr.BXY=2 ...(I)
In s ABC and BXY,
XBY=ABC (Common angle)
BXY=BAC (Corresponding angles of parallel lines XY and AC)
BYX=BCA (Corresponding angles of parallel lines XY and AC)
ABCXBY (AAA postulate)
Now, Ar.ABCAr.BXY=AB2BX2 (Similar triangle Property)
2=AB2BX2
ABBX=2
AB=2BX
AX+XB=2XB
AX=(21)XB
AX:XB=(21):1

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