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mexican regional collinearity

Source: 2024 Mathematics Regional Olympiad of Mexico West P2

October 21, 2024

geometrycollinear

Problem Statement

Let

\triangle ABC

be a triangle and

H

its orthocenter. We draw the circumference

\mathcal{C}_1

that passes through

H

and its tangent to

BC

at

B

and the circumference

\mathcal{C}_2

that passes through

H

and its tangent to

BC

at

C

. If

\mathcal{C}_1

cuts line

AB

again at

X

and

\mathcal{C}_2

cuts line

AC

again at

Y

. Prove that

X,Y

and

H

are collinear.

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