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angle independent of the point X, starting with cyclic trapezoid

Source: Cono Sur Shortlist 2009 G2

July 26, 2019

trapezoidisoscelesCyclicfixedanglegeometry

Problem Statement

The trapezoid

C

, of bases

AB

and

CD

, is inscribed in a circumference

\Gamma

. Let

X

a variable point of the arc

AB

of

\Gamma

that does not contain

C

or

D

. We denote

Y

to the point of intersection of

AB

and

DX

, and let Z be the point of the segment

CX

such that

\frac{XZ}{XC}=\frac{AY}{AB}

. Prove that the measure of

\angle AZX

does not depend on the choice of

X.

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