Intersecting Chords Theorem (Extension)

This is an extension from "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 lines AB and CD intersect at the point T.

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 AB and CD

Instructions:

1. Adjust the positions of the points C and D such that they coincide and the lengths of CT = DT.
2. Recall which theorem this is.
3. Repeat steps 1 ~ 2 for other positions and lengths of CT = DT.
4. Adjust the positions of the points A, B, C and D such that AB and CD intersect outside the circle.
5. Check the box.
6. Observe the values of \(AT \times BT\) and \(CT \times DT\).
7. Repeat steps 4 ~ 6 for other positions and lengths of AB and CD.

Download the GeoGebra file: http://www.geogebratube.org/material/download/format/file/id/36097

Download the Worksheet: http://db.tt/UDNAb4v7

Note: When AB and CD intersect outside the circle, this theorem is known as the "Secant-Secant Theorem".