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Isotomic points on line joining incenters

Source: International Zhautykov Olympiad 2018/2

January 12, 2018

geometryincenterKvant

Problem Statement

Let

N,K,L

be points on the sides

\overline{AB}, \overline{BC}, \overline{CA}

respectively. Suppose

AL=BK

and

\overline{CN}

is the internal bisector of angle

ACB

. Let

P

be the intersection of lines

\overline{AK}

and

\overline{BL}

and let

I,J

be the incenters of triangles

APL

and

BPK

respectively. Let

Q

be the intersection of lines

\overline{IJ}

and

\overline{CN}

. Prove that

IP=JQ

.

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