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Question

In ΔABC, ¯¯¯¯¯¯¯¯¯XY is parallel to ¯¯¯¯¯¯¯¯AC and divides the triangle into the two parts of equal area. Then the AXAB equals:
613389_c10d9667b6a9461bb58f79f63f925364.PNG

A
2+12
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B
222
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C
2+22
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D
212
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Solution

The correct option is B 222
Given that XY is parallel to AC

Area of triangle BXY=12×BX×BY×sinB

Area of triangle ABC=12×AB×BC×sinB

We have 12×AB×BC×sinB=2×12×BX×BY×sinB

BXBA×BYBC=12

BXBA=12

Therefore AXAB=1BXAB=112=212

multiplying numerator and denominator by 2

=222

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