This is another problem from MEI’s MathsMonday.

“Two equilateral triangles share a common vertex. Show that the lengths marked a and b are equal for any such arrangement.”

This seems quite amazing at first.  One can picture the small triangle swinging back and forth with red bungee chords tethering its bottom vertices to the bottom vertices of the large triangle.  It would seem remarkable that the lengths of the chords would remain equal to each other throughout.

See the Tethered Triangle Puzzle