Angles in Alternate Segments

Below shows a circle, with centre O.
The points A, B, C and X are points on the circumference of the circle.
The line PQ is the tangent to the circle at A.

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 segment ACB
• shift the point C to change its position

Instructions:

1. Adjust the position and size of the segment ACB.
2. Adjust the position of the point C.
3. Check all boxes.
4. Observe the angle in the (alternate) segment ACB (i.e. ∠ACB) and the angle formed by the chord AB and the tangent PQ (i.e. ∠BAQ).
5. Repeat steps 1 ~ 4 for other positions and sizes of the segment ACB and the point C.

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



Download the GeoGebra file: http://www.geogebratube.org/material/download/format/file/id/41894

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

Note: This property is also known as "Alternate Segment Theorem".