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Question

In a triangle ABC, points X and Y are on AB and AC, respectively, such that XY is parallel to BC. Which of the two following always hold(s) good? (Here [PQR] denotes the area of triangle PQR.)

(I) [BCX] = [BCY]

(II) [ACX] .[ABY] = [AXY] .[ABC] 



A

Neither [I] nor [II]

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B

[I] only

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C

[II] only

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D

both [I] and [II]

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Solution

The correct option is D

both [I] and [II]


ΔBCX=ΔBCY (Obvious)

Same base and same height

Now Let A(O),AB=b,AC=c

So AX=λb,AY=λc

ΔACX=12λ|b×c|

ΔABY=12λ|b×c|

ΔAXY=12λ2|b×c|

ΔABC=12|b×c|


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