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Prove an angle

Source: Indian RMO 2001 Problem5

October 27, 2005

geometrycircumcircletrigonometrycongruent triangles

Problem Statement

In a triangle

ABC

D

is a point on

BC

such that

AD

is the internal bisector of

\angle A

. Suppose

\angle B = 2 \angle C

and

CD =AB

. prove that

\angle A = 72^{\circ}