Question

ABC is a triangle on which AB=AC and D is a point on AC such that BC2 = AC*CD prove that BD=BC

Answer 1

Given: A △ABC in which AB = AC. D is a point on AC such that BC2 = AC × CD.
To prove : BD = BC 
Proof : Since BC2 = AC × CD
Therefore BC × BC = AC × CD
AC/BC = BC/CD .......(i)
Also ∠ACB = ∠BCD
Since △ABC ~ △BDC [By SAS Axiom of similar triangles]
AB/AC = BD/BC ........(ii)
But AB = AC (Given) .........(iii)
From (i),(ii) and (iii) we get 
BD = BC.