Tangent-Secant Theorem

Below shows a circle, with centre O.
The points A, B, C and X are points on the circumference of the circle.
The line ABT is a secant of the circle and the line CT is a tangent 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, B and C to change their positions and the lengths of the secant ABT and tangent CT

Instructions:

1. Adjust the positions and lengths of the secant ABT and tangent CT.
2. Check the box.
3. Observe the values of \(AT \times BT\) and \(C{T^2}\).
4. Repeat steps 1 ~ 3 for other positions and lengths of the secant ABT and tangent CT.

Download the GeoGebra file: http://www.geogebratube.org/material/download/format/file/id/36098

Download the Worksheet: http://db.tt/9FFZRETK