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Question

In given figure ABC is an isosceles triangle with AB=AC and D is a point on AC such that BC2=AC×CD. Prove that BD=BC.
1008980_6d8068cceb26414e983ea507a1150990.png

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Solution

We have,

BC2=AC×CD and AB=AC

BC×BC=AC×CD and B=C

BCAC=CDBC and B=C

BCCA=DCCB and B=C

So, by SAS-criterion of similarity, we have

BCADCB

BCDC=CACB=BADB

CACB=BADB

BACA=DBCB

1=DBCB [ BA=CA]

DB=CB

BD=BC [Hence proved]


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