Abc Is Triangle In Which Ab Ac And D Is Point On Side Ac Such That Bc2 Ac Cd Prove That Bd Bc

ABC is a triangle in which AB = Ac and D is a point on the side AC such that BC2 = AC × CD. Prove that BD = BC.

Answers:

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.