MathDB

2008 JBMO Shortlist G10

Source: 2008 JBMO Shortlist G10

October 10, 2017

geometryJBMO

Problem Statement

Let

\Gamma

be a circle of center

O

, and

\delta

. be a line in the plane of

\Gamma

, not intersecting it. Denote by

A

the foot of the perpendicular from

O

onto

\delta

., and let

M

be a (variable) point on

\Gamma

. Denote by

\gamma

the circle of diameter

AM

, by

X

the (other than M ) intersection point of

\gamma

and

\Gamma

, and by

Y

the (other than

A

) intersection point of

\gamma

and

\delta

. Prove that the line

XY

passes through a fixed point.

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