The Butterfly Explored by:

Aubrey D. Johnson

. Through the Midpoint of any chord PQ of a circle, any chords AB and CD are drawn; lines AD and BC meet PQ at points X and Y. You may want to construct a line PQ containing the chord PQ. Prove that M is the midpoint of XY.

For M to be the midpoint of XY, XM = MY. Using the GSP to calculate, let us see if this is so.

And for the most part they do equal.