butterfly theorem

Let $M$ be the midpoint of a chord $PQ$ of a circle, through which two other chords $AB$ and $CD$ are drawn. If $AD$ intersects $PQ$ at $X$ and $CB$ intersects $PQ$ at $Y$,then $M$ is also the midpoint of $XY.$

The theorem gets its name from the shape of the figure, which resembles a butterfly.

Title butterfly theorem ButterflyTheorem 2013-03-22 13:10:06 2013-03-22 13:10:06 giri (919) giri (919) 8 giri (919) Theorem msc 51-00