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.

**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.