Angles between Tangents & Radii

Below shows a circle, with centre O.
The points P and X are points on the circumference of the circle.
The line AB is the tangent to the circle at P.

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 the box.
3. Observe ∠OPB.
4. Repeat steps 1 ~ 3 for other positions of the point P.

Note: To see the animation, check the box, then click on the "play" button (at bottom left).



Download the GeoGebra file: http://www.geogebratube.org/material/download/format/file/id/41089

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