The askew envelope

In a square, an interior point is drawn with an angle to the top vertices of 120°. What’s the angle between the chords formed by the two arcs centered in these vertices?

Scroll down for a solution to this problem.


The angle β is also 120°.

The solution follows from straightforward angle propagation. Start with α in the right corner of the dark triangle. Use the fact that:

  • angles in a triangle add up to 180
  • the chord triangles are both isosceles
  • the two bottom angles in an isosceles triangle are equal

Now β=360-120-(45+α/2)-(75-α/2)=120.

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