Question

In a ΔABC, AB = AC and D is a point on side AC, such that BC2

= AC × CD. Prove that BD =

BC.

Answer 1

construct the middle point to AB say E.

consider the ∆ABD & ∆BDC

AE=AD (AS E AND D ARE MID POINTS)

BD=BD(COMMON SIDE)

BE=CD(AS E AND D ARE MID POINTS)

SO ∆ABD is congruent to ∆BDC.

SO BD=BC(CPCT)