IMO 1986 LL CAN9

In a triangle ABC, ngleBAC = 100◦, AB = AC. A point

IMO 1986 LL CAN9

Origin: CAN

Problem

In a triangle ABC, \angleBAC = 100◦, AB = AC. A point D is chosen on the side AC such that \angleABD = \angleCBD. Prove that AD + DB = BC.