External Points of Circles

Below shows a circle, with centre O.
The points A, B and X are points on the circumference of the circle.
The point P is a point outside of the circle.
The lines AP and BP are tangents to the circle at points A and B respectively.

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 point P to change its position

Instructions:

1. Adjust the position of the point P.
2. Check all boxes.
3. Observe the lengths of the tangents from the point P (i.e. AP and BP), ∠APO & ∠BPO and ∠AOP & ∠BOP.
4. Repeat steps 1 ~ 3 for other positions of the point P.

Download the GeoGebra file: http://www.geogebratube.org/material/download/format/file/id/41110

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