Three Random Points on a Circle

The problem
three uniformly random points on a circleP(triangle is acute) = ?

Pick three points uniformly at random on a circle. They form a triangle.

What is the probability that the triangle is acute — i.e. all three angles are less than 90°90°?

Tempting (but wrong)
"most triangles look acute — ½? ¾?"but the math gives one quarter

Acute triangles feel like the typical case — most random-looking triangles aren't extremely stretched. People usually guess between 12\tfrac{1}{2} and 34\tfrac{3}{4}.

But the geometry of inscribed triangles is much more constraining than free-floating triangles, and the answer is far below 50%.