MathDB

P2 Cono Sur 2021

Source: Cono Sur 2021 P2

November 30, 2021

geometryCyclic Quadrilateralstriangle -incentercircumcircle

Problem Statement

Let

ABC

be a triangle and

I

its incenter. The lines

BI

and

CI

intersect the circumcircle of

ABC

again at

M

and

N

, respectively. Let

C_1

and

P

be the circumferences of diameters

NI

and

MI

, respectively. The circle

C_1

intersects

AB

at

P

and

Q

, and the circle

C_2

intersects

AC

at

R

and

S

. Show that

P

,

Q

,

R

and

S

are concyclic.

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