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Geometry

Source: Sharygin Oral Geometry Olympiad 2017.Senior League(10-11) P6

April 16, 2017

geometrycircumcircle

Problem Statement

Given acute angled traingle

ABC

and altitudes

AA_1

,

BB_1

,

CC_1

. Let

M

midpoint of

BC

.

P

point of intersection of circles

(AB_1C_1)

and

(ABC)

.

T

is point of intersection of tangents to

(ABC)

at

B

and

C

.

S

point of intersection of

AT

and

(ABC)

. Prove that

P,A_1,S

and midpoint of

MT

collinear.

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