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altitudes and circles tangent to the circumcircle

Source: Tuymaada 2007, Problem 3

July 15, 2007

geometrycircumcircleGauss

Problem Statement

AA_{1}

,

BB_{1}

,

CC_{1}

are altitudes of an acute triangle

ABC

. A circle passing through

A_{2}

and

B_{2}

touches the arc

AA_{2}

of its circumcircle at

C_{2}

. The points

A_{2}

,

B_{2}

are defined similarly. Prove that the lines

AA_{2}

,

BB_{2}

,

CC_{2}

are concurrent.

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