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Junior Geometric Inequality with <BAC=60

Source: JBMO Shortlist 2013, G5

June 11, 2017

geometrygeometric inequality

Problem Statement

A circle passing through the midpoint

M

of the side

BC

and the vertex

A

of the triangle

ABC

intersects the segments

AB

and

AC

for the second time in the points

P

and

Q

, respectively. Prove that if

\angle BAC=60^{\circ}

, then

AP+AQ+PQ<AB+AC+\frac{1}{2} BC

.

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