Random Triangles

How often is a triangle acute?

An interactive lesson with 6 steps, about 5 minutes: you predict, drag and solve, with instant feedback on every answer. It runs in your browser and needs JavaScript.

What you’ll learn

• An inscribed triangle is acute exactly when it contains the centre.
• Three random points lie in a semicircle with probability 3/4.
• So only 1 in 4 random inscribed triangles is acute.

Steps

1. Three points on a circle
2. Make a right angle
3. The semicircle test
4. Count them
5. The answer
6. Four points