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2024 Portuguese MO Finals Day 2 P4

Source: 2024 Portuguese MO Finals Day 2 P4

March 24, 2024

geometry

Problem Statement

A circle inscribed in the square

ABCD

, with side

10

cm, intersects sides

BC

and

AD

at points

M

and

N

respectively. The point

I

is the intersection of

AM

with the circle different from

M

, and

P

is the orthogonal projection of

I

into

MN

. Find the value of segment

PI

.

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