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Prove that UV || CA

Source: problem 2 (G2) of QEDMO 1; created by myself

November 7, 2005

geometrygeometric transformationreflectiongeometry proposed

Problem Statement

Let

ABC

be a triangle. Let

C^{\prime}

and

C^{\prime}

be the reflections of its vertices

BC

and

A

, respectively, in the altitude of triangle

ABC

issuing from

B

. The perpendicular to the line

BA^{\prime}

through the point

C^{\prime}

intersects the line

UV \parallel CA

at

U

; the perpendicular to the line

BC^{\prime}

through the point

A^{\prime}

intersects the line

BA

at

V

. Prove that

UV \parallel CA

. Darij

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