**In a triangle ABC, AB = AC and D is a point on side AC such that BC²**** = AC x CD, Prove that BD = BC.**

**Solution:**

**More Solutions:**

- If the diagonal AC bisects A, then prove that:
- Prove that it is a square.
- Show that ABCD is a square.
- Show that PQ is bisected at O.
- Show that AC and PQ bisect each other.
- Prove that AP and DQ are perpendicular to each other.
- Prove that CQ || AP.
- The four bisectors form a quadrilateral ABCD.
- The bisector of ∠A meets DC in E and AB = 2 AD.
- A and B meet at E which lie on DC.