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The line t through the centroid of triangle ABC

Source: Baltic Way 2006

December 4, 2010

geometrycircumcircletrapezoidgeometry proposed

Problem Statement

Let the medians of the triangle

ABC

intersect at point

M

. A line

t

through

M

intersects the circumcircle of

ABC

at

X

and

Y

so that

A

and

C

lie on the same side of

t

. Prove that

BX\cdot BY=AX\cdot AY+CX\cdot CY

.

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