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Reflection of foot of altitudes

Source: Azerbaijan NMO 2024. Senior P3

July 8, 2024

geometryAZE JUNIOR NATIONAL MOAZE SENIOR NATIONAL MO

Problem Statement

In a scalene triangle

C

, the points

E

and

F

are the foot of altitudes drawn from

B

and

C

, respectively. The points

X

and

Y

are the reflections of the vertices

B

and

C

to the line

EF

, respectively. Let the circumcircles of the

\triangle ABC

and

\triangle AEF

intersect at

T

for the second time. Show that the four points

A, X, Y, T

lie on a single circle.

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