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
Canonical name	ButterflyTheorem
Date of creation	2013-03-22 13:10:06
Last modified on	2013-03-22 13:10:06
Owner	giri (919)
Last modified by	giri (919)
Numerical id	8
Author	giri (919)
Entry type	Theorem
Classification	msc 51-00