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2021china tst pure geo3

Source: 2021ChinaTST test4 day1 P2

April 13, 2021

geometryHarmonics

Problem Statement

Let triangle

ABC(AB<AC)

with incenter

I

circumscribed in

\odot O

. Let

M,N

be midpoint of arc

\widehat{BAC}

and

\widehat{BC}

, respectively.

D

lies on

\odot O

so that

AD//BC

, and

E

is tangency point of

A

-excircle of

\bigtriangleup ABC

. Point

F

is in

\odot O

so that

FI//BC

and

\angle BAF=\angle EAC

. Extend

NF

to meet

\odot O

at

G

, and extend

AG

to meet line

IF

at L. Let line

AF

and

DI

meet at

K

. Proof that

ML\bot NK

.

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