Theorem of the Day Glossary icon

Java applet illustrating The Five Circle Theorem

interactive Morley triangles
Test the theorem with this applet, created using David Joyce's Geometry Applet software. Move the circle on points X, Y and Z until they lie exactly on any three distinct points of intersection of the circles, other than the points A, B, C, D and E of the pentagon. You will find that two other circle intersections are automatically included! Move the points P, Q, R, S and T to set yourself a new challenge!

 

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