In a triangle ABC , AB =AC  and D is a point on side AC , such that BC2=AC.CD . Prove that BD =BC . PLEASE HELP ME MERITNATION !!! 

given:BC2=AC.CD,BC/AC=CD/BC AND AB=AC

TO PROVE=BD=BC

PROOF;

IN TRIANGLES ACB AND BCD

BC/AC=CD/BC  (GIVEN)

 ANGLE C=ANGLE C  (COMMON)

THEN TRIANGLE ACB ~ TRIANGLE BCD

BD/AB=BC/AC

BD=BC  (AB=AC)

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