WOLFRAM|DEMONSTRATIONS PROJECT

The Butterfly Theorem

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AP
0.61
PB
0.61
A
B
P
C
D
E
F
G
H

Let HE be a chord of a circle and CF and DG be two other chords passing through the midpoint P of HE. If CG and DF intersect HE, denote the points of intersection by A and B. When CG and DF intersect HE, P is the midpoint of AB.

Drag any of the magenta points on the circle to modify the diagram.