Intersecting Chords Theorem

Below shows a circle, with centre O.
The points A, B, C, D and X are points on the circumference of the circle.
The chords AB and CD intersect at the point T (inside 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, B, C and D to change their positions and the lengths of the chords AB and CD

Instructions:

1. Adjust the positions and lengths of the chords AB and CD.
2. Check the box.
3. Observe the values of \(AT \times BT\) and \(CT \times DT\).
4. Repeat steps 1 ~ 3 for other positions and lengths of the chords AB and CD.

Download the GeoGebra file: http://www.geogebratube.org/material/download/format/file/id/36095

Download the Worksheet: http://db.tt/AbN2zjBl

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