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A B C is an isosceles triangle with A B=...

`A B C` is an isosceles triangle with `A B=A C` and `D` is a point on `A C` such that `B C^2=A CxxC Ddot` Prove that `B D=B C`

Text Solution

Verified by Experts

we have
`BC^(2)= ACxxCD and AB = AC`
`BC xx BC = AC xx CD and angleB = angleC`
There may be 3 possibilities:

` Rightarrow triangleBCD ~triangleABC` ( by SAS criterion)
`(BC)/(AB)= (CD)/(BC)= (BD)/(AC)`
`(BC) /(AB) = (BD)/(AC)`
BC=BD (AB= AC, given) Hence proved
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