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Easy geometry from Taiwan TST

Source: 2017 Taiwan TST Round 1

April 13, 2018

geometry

Problem Statement

Two line

BC

and

EF

are parallel. Let

D

be a point on segment

BC

different from

B

,

C

. Let

I

be the intersection of

BF

ans

CE

. Denote the circumcircle of

\triangle CDE

and

\triangle BDF

as

K

,

L

. Circle

DF

,

L

are tangent with

EF

at

E

,

F

,respectively. Let

A

be the other intersection of circle

K

and

L

. Let

DF

and circle

K

intersect again at

Q

, and

DE

and circle

L

intersect again at

R

. Let

EQ

and

FR

intersect at

M

.\\ Prove that

I

,

A

,

M

are collinear.

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