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9th ibmo - brazil 1994/q4.

Source: Spanish Communities

May 7, 2006

geometrycircumcirclegeometry unsolved

Problem Statement

Let

A,\ B

and

C

be given points on a circumference

K

such that the triangle

\triangle{ABC}

is acute. Let

P

be a point in the interior of

K

.

X,\ Y

and

Z

be the other intersection of

AP, BP

and

CP

with the circumference. Determine the position of

P

such that

\triangle{XYZ}

is equilateral.

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