MathDB

2009 JBMO Shortlist G3

Source: 2009 JBMO Shortlist G3

October 8, 2017

geometryJBMO

Problem Statement

Parallelogram

{ABCD}

with obtuse angle

\angle ABC

is given. After rotation of the triangle

{ACD}

around the vertex

{C}

, we get a triangle

{CD'A'}

, such that points

B,C

and

{D'}

are collinear. Extensions of median of triangle

{CD'A'}

that passes through

{D'}

intersects the straight line

{BD}

at point

{P}

. Prove that

{PC}

is the bisector of the angle

\angle BP{D}'

.

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