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Ratio of division of line perpendicular to $OI$

Source: Sharygin Geometry Olympiad, Final Round 2016, Problem 3 grade 9

August 4, 2016

geometry

Problem Statement

Let

O

and

I

be the circumcenter and incenter of triangle

ABC

. The perpendicular from

I

OI

meets

AB

and the external bisector of angle

C

at points

X

and

Y

respectively. In what ratio does

I

divide the segment

XY