Morley's Miracle

This GeoGebra applet demonstrates the famous theorem discovered by Frank Morley towards the end of the nineteenth century.

Triangle ABC is arbitrary. Each internal angle of the triangle is trisected, and the trisectors meet at points P, Q and R, as shown (the trisectors closest to BC meet at P, the trisectors closest to CA meet at Q, and the trisectors closest to AB meet at R).

And now the miracle: triangle PQR is equilateral, regardless of the shape of triangle ABC!


Sorry, the GeoGebra Applet could not be started. Please make sure that Java 1.4.2 (or later) is installed and active in your browser (Click here to install Java now)


You can test it out by dragging the vertices using the mouse!

For more on Frank Morley, you can study the Wikipedia site MorleyWiki: or this site: MorleyBiography. I was impressed by the fact that he was a very good chess player and even managed to beat the great Emanuel Lasker while Lasker was the World Chess Champion.