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ABC is atriangle in which AB=AC and D is a point on AC such that BC^2=AC*CD.

prove that BD=BC

Asked by pugalatha | 12th Sep, 2015, 11:43: PM

Expert Answer:

$C o n s i d e r space t h e space f o l o w i n g space f i g u r e.$

$G v i e n space t h a t space B C squared equals A C cross times C D rightwards double arrow fraction numerator B C over denominator C D end fraction equals fraction numerator A C over denominator B C end fraction... left parenthesis 1 right parenthesis A n d space a n g l e space angle C space i s space c o m m o n space t o space b o t h space t h e space t r i a n g l e s space triangle A B C space a n d space triangle B D C$

$therefore B y space S A S space s i m i l a r i t y comma space triangle A B C tilde triangle D B C rightwards double arrow fraction numerator A B over denominator D B end fraction equals fraction numerator B C over denominator D C end fraction rightwards double arrow fraction numerator A C over denominator D B end fraction equals fraction numerator B C over denominator D C end fraction space space space space space space open square brackets g i v e n space A B equals A C close square brackets... left parenthesis 2 right parenthesis F r o m space e q u a t i o n s space left parenthesis 1 right parenthesis space a n d space left parenthesis 2 right parenthesis comma space w e space h a v e comma fraction numerator A C over denominator D B end fraction equals fraction numerator A C over denominator B C end fraction rightwards double arrow B D equals B C$

Answered by Vimala Ramamurthy | 13th Sep, 2015, 07:25: PM

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