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°).
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  • 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