MathDB

Angles and excenters

Source: Kürschák 2012, problem 1

July 4, 2015

geometry

Problem Statement

Let

J_A

and

J_B

be the

A

-excenter and

B

-excenter of

\triangle ABC

. Consider a chord

\overline{PQ}

of circle

ABC

which is parallel to

AB

and intersects segments

\overline{AC}

and

\overline{BC}

. If lines

AB

and

CP

intersect at

R

, prove that

\angle J_AQJ_B+\angle J_ARJ_B=180^\circ.

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