Angles in a Semicircle

Thales’ theorem

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 angle inscribed in a semicircle is always 90° (Thales’ theorem).
• Conversely, a right angle on a circle subtends a diameter.
• This gives a practical way to find a circle’s centre.

Steps

1. Across the diameter
2. Triangle in a semicircle
3. Right angles everywhere
4. A rectangle in a circle
5. The circumcircle
6. Find the centre