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Question

In ABC, PQ is a line segment intersecting AB at P and AC at Q such that PQ BC and PQ divides ABC into two parts equal in area. Find BPAB.

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Solution


Since the line PQ divides ABC into two equal parts,


area(APQ)=area(BPQC)


area(APQ)=area(ABC)area(APQ)


2area(APQ)=area(ABC)


area(ABC)area(APQ)=21 ---- ( 1 )


Now, in ABC and APQ,


BAC=PAQ [ Common angles ]


ABC=APQ [ Corresponding angles ]


ABCAPQ [ By AA similarity ]


area(ABC)area(APQ)=AB2AP2


21=AB2AP2 [ From ( 1 ) ]


ABAP=21


ABBPAB=12


1BPAB=12


BPAB=112


BPAB=212



930919_969441_ans_9f58e157867c4088bace14f2221ab7da.png

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