Thursday, January 10, 2013

GeoGebra Tutorial: Constructing a Cardioid

A cardioid is a curve formed by moving circles. One of the ways to form a cardioid is shown below. In the applet (move the slider to the extreme right), the cardioid is given as the envelope of circles whose centers lie on a given circle and which pass through a fixed point on the given circle. 

This is a Java Applet created using GeoGebra from - it looks like you don't have Java installed, please go to

Step by Step Instruction in Constructing the Applet Above

1. Construct point A at (0,0) and point B at (0,1).
2. Construct a circle with center A and passing through B
3. Construct an angle slider and set the minimum number to 0°, maximum number to 360° degrees and increment of 2°.  
4. Construct angle BAB'. To do this, select the Angle with Given Size tool, click on point B and click on point A to display the Angle with Given Size dialog box. 
5. In the Angle with Given Size dialog box, replace 45° with α,  choose counterclockwise button, and then click OK. 
6. Hide the green sector by right clicking it and then clicking on the Show Object from the pop up menu.
7. Now construct a circle with center B' and passing through B.
8. Right click the circle with center B and  click Trace on. 
9. Move the slider and observe what happens.