Thales Theorem - Circles, Diameters and Right Triangles

Thale's Theorem: Let A, B, C be 3 points on a circle where \overline{\color{green}A\color{blue}C} is a diameter of the circle. Then \angle ABC is a right angle and ΔABC is a right-triangle.

Interactivity

Click and drag B to see that \angle ABC is always a right angle (90°).

You can click and drag any point except A. Why do you think you cannot drag A?

DIY: Construct Thale's Theorem Directions

1. Use Circle through center and point tool and draw a circle c.
2. Use Line tool to draw a line through both points A and B.
3. Use Intersect tool to find the intersection point C between the circle and the line a. This makes the segment BC a diameter!
4. Use Point tool and draw any point D on the circle.
5. Use Polygon tool to draw triangle CDB.
6. Select Angle through 3 points tool - click inside the triangle. All angles will be marked.

Notice that angle CDB is a right angle.

Use

Move tool and click and drag point D. Angle CDB remains a right angle.

Up one level
This work is licensed under a Creative Commons Attribution-Share Alike 3.0 United States License.