# 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°). This browser does not have a Java Plug-in. Get the latest Java Plug-in here. 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.

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Page last modified on November 25, 2009, at 01:18 AM