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Turkey NMO 2007 Problem 5, CY=2MK

Source: Turkey NMO 2007 Problem 5

September 27, 2011

geometryincentercircumcircleinradiusrectanglegeometry unsolved

Problem Statement

Let

ABC

be a triangle with

\angle B=90

. The incircle of

ABC

touches the side

BC

at

D

. The incenters of triangles

ABD

and

ADC

are

X

and

Z

, respectively. The lines

XZ

and

AD

are intersecting at the point

K

.

XZ

and circumcircle of

ABC

are intersecting at

U

and

V

. Let

M

be the midpoint of line segment

[UV]

.

AD

intersects the circumcircle of

ABC

at

Y

other than

A

. Prove that

|CY|=2|MK|

.

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