Angles in Opposite Segments

Below shows a circle, with centre O.
The points A, B, C, D and X are points on the circumference of the circle.

You can:

• shift the point O to change the position of the circle
• shift the point X to change the size of the circle
• shift the points A and B to change the position and size of the segments ACB and ADB
• shift the points C and D to change their positions

Instructions:

1. Adjust the positions and sizes of the segments ACB and ADB.
2. Adjust the positions of the points C and D.
3. Check the box.
4. Observe the angles in the (opposite) segments ACB and ADB (i.e. ∠ACB and ∠ADB respectively).
5. Repeat steps 1 ~ 4 for other positions and sizes of the segments ACB and ADB, and the points C and D.

Note: To see the animation, check the box, then click on the "play" button (at bottom left).



Download the GeoGebra file: http://www.geogebratube.org/material/download/format/file/id/41088

Download the Worksheet: http://db.tt/2USPPMtV

Note: The quadrilateral formed by the points A, B, C and D is also called a "Cyclic Quadrilateral".