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Question

In the figure, XYAC and XY divides the triangular region ABC into two equal areas.Determine AX:AB.

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Solution

It is given that XY divides the triangular region ABC into two equal areas.That means A(BXY)=A(AXYC)A(BXY)A(AXYC)=11A(BXY)A(BAC)-A(BXY)=112A(BXY)=A(BAC)A(BXY)A(BAC)=12 ...(1)It is given that XYAC.InBXY andBAC,BXY=BAC [Corresponding angles]BYX=BCA [Corresponding angles]Therefore, by AA similarity testBXY ~BACNow, we can say thatA(BXY)A(BAC)=BXAB212=BXAB2 [From (1)]AB-AXAB2=12AB21-AXAB2AB2=12

1-AXAB = 12AXAB =1- 12AXAB = 2-12

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