MathDB

The circumcenter

Source: IMO Shortlist 1994, G3

October 22, 2005

geometrycircumcircleinradiussymmetryincenterIMO Shortlist

Problem Statement

A circle

C

has two parallel tangents

L'

and

L"

. A circle

C'

touches

C

at

A

and

C

at

Z

. A circle

AY

touches

BX

at

B

,

C

at

Y

and

C'

at

Z

. The lines

AY

and

BX

meet at

Q

. Show that

Q

is the circumcenter of

XYZ

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