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Question

ABCD is a parallelogram with diagonal AC. If a line XY is drawn such that it cuts the side AD at point Z and XY || AB, thenBXXC can be equal to:


A

AYAC

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B

DZAZ

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C

AZZD

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D

AYYC

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Solution

The correct options are
C

AZZD


D

AYYC


Consider ΔABC,

ABXY

BXXC=AYYC...(i) (By Basic proportionality theorem)

Consider parallelogram ABCD, AB || CD(Opposite sides of a parallelogram areparallel)

ABCDXZ

Consider ΔACD,

CDYZ

AYYC=AZZD...(ii) (By Basic proportionality theorem)

From (1) and (2),
BXXC=AYYC=AZZD


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