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2015 Taiwan TST Round 1 Mock IMO Day 2 Problem 1

Source: 2015 Taiwan TST Round 1 Mock IMO Day 2 Problem 1

July 12, 2015

Taiwangeometrycircumcirclegeometric transformationreflectionTaiwan TST 2015

Problem Statement

Let

ABC

be a triangle and

M

be the midpoint of

BC

, and let

AM

meet the circumcircle of

ABC

again at

R

. A line passing through

R

and parallel to

BC

meet the circumcircle of

ABC

again at

S

. Let

U

be the foot from

R

to

BC

, and

T

be the reflection of

U

in

R

.

D

lies in

BC

such that

AD

is an altitude.

N

is the midpoint of

AD

. Finally let

AS

and

MN

meets at

K

. Prove that

AT

bisector

MK

.

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