Question

In triangle ABC, AB=AC&D is a point on side AC, such that BC^2=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.