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Poncelet Porism configuration

Source: Kvant Magazine No. 3 2022 M2692

March 8, 2023

Kvantgeometryporismhexagon

Problem Statement

In the circle

\Omega

the hexagon

ABCDEF

is inscribed. It is known that the point

D{}

divides the arc

BC

in half, and the triangles

ABC

and

AB

have a common inscribed circle. The line

BC

intersects segments

Z

and

DE

at points

X

and

Y

and the line

EF

intersects segments

AB

and

AC

at points

Z

and

T

respectively. Prove that the points

X, Y, T

and

Z

lie on the same circle.
Proposed by D. Brodsky

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