The new normal

Two equilateral triangles are placed as shown. Their centres are connected as well as their intersection points. What’s the angle α?

Scroll down for a solution to this problem.


The angle α is 90°.

Solution by mathsfrog.

Note that this solution makes clever use of the radical axis where the points have equal power with respect to the two circumcircles.

This puzzle was conceived in close collaboration with Marshall W. Buck. It can be generalized to two similar triangles having their circumcentres connected.

Generalized version

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One reply on “The new normal”

The use of the radical axis in the previous problem was intended to be a hint to the solution of this one.

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