Alternate Segment Theorem

Chord: It is a straight line from a point on its circumference to another point on its circumference.

Tangent: It is a straight line that touches the circle at a point on its circumference.

Secant: It is a straight line passing through a circle at two distinct points.

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/i79YKpwI

Note: This theorem is also known as the "Tangent-Chord Theorem".