Question

In a triangle ABC, AB = AC and D is a point on the side AC suck that BC 2 = AC*AD. Prove that BD = BC

Answer 1

Answer:

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.