Question

In a triangle ABC, AB=AC and D is a point on side AC such that BC square = AC*CD. Prove that BD=BC.​

Answer 1

The ratio of corresponding sides may be written in extended way as follows

B

C

C

D

=

A

C

B

C

=

A

B

B

D

From this relation we have

A

C

B

C

=

AB

BD

⇒

AC

BC=

AC

BD→

As AB

=AC

given

⇒1

BC=1

BD

⇒

BC=BD

Proved

Hope, this will help