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P,N,S are collinear

Source: Sharygin CR P9(Grades 8-9)

March 4, 2022

Sharygin Geometry OlympiadSharygin 2022geometry

Problem Statement

The sides

AB, BC, CD

and

DA

of quadrilateral

ABCD

touch a circle with center

I

at points

K, L, M

and

N

respectively. Let

P

be an arbitrary point of line

AI

. Let

PK

meet

BI

at point

Q, QL

meet

CI

at point

R

, and

RM

meet

DI

at point

S

. Prove that

P,N

and

S

are collinear.

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