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<A=? if BC = BD + AD in isosceles ABC, angle bisector

Source: 2004 All-Ukrainian Correspondence MO of magazine ''In the World of Mathematics'', grades 5-11 p10

April 28, 2021
geometryisoscelesUkraine Correspondence

Problem Statement

In an isosceles triangle ABCABC (AB=ACAB = AC), the bisector of the angle BB intersects ACAC at point DD such that BC=BD+ADBC = BD + AD. Find A\angle A.