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midpoints of 2 arcs, point on arc,2 incenters, similar triangles wanted

Source: Moldova 2002 TST 2 P3

August 25, 2018

geometryincentersimilar trianglesarc

Problem Statement

A triangle

ABC

is inscribed in a circle

G

. Points

M

and

N

are the midpoints of the arcs

BC

and

AC

respectively, and

D

is an arbitrary point on the arc

AB

(not containing

C

). Points

I_1

and

I_2

are the incenters of the triangles

ADC

and

BDC

, respectively. If the circumcircle of triangle

DI_1I_2

meets

G

again at

P

, prove that triangles

PNI_1

and

PMI_2

are similar.