# Operations on a unit circle [duplicate]

For a mathematical problem I have to work with mathematica, but I am not really familiar with mathematica. Can someone help me with the following?

Step 1: Make a function f(u) of one parameter, u, which does the following:

• Draws a circle with radius 1 (a unit circle), which touches the x-axis in the origin. So with center (0,1).

• Draws the x-axis and the y-axis.

• Draws the circles with radius u that touch the x-axis and this unit circle, with center not on the y-axis.

Hint: How many of these circles are there?

• Draws 1) the centers of these circles, 2) the connecting line between the centers of these circles and the center of the unit circle. Furthermore it should draw 3) the lines between the centers of these circles and the projections of these centers onto the x-axis.

• Makes sure the relevant points have letters, as well as the relevant line segments (properly besides the middle of the line segments).

Step 2:

• Draw the curve which runs through the center of the circles in the (x,y)-plane.
• Choose a certain radius u and make the sketched figure by using the function f .
• What have you tried yourself this far? Commented Apr 2, 2018 at 10:19
• I have already made a unit circle and plot all circles that touch the x-axis and the unit circle, but I am not sure if it is a function. Commented Apr 2, 2018 at 10:55
• This sounds like homework ....
– Alan
Commented Apr 2, 2018 at 12:42
• "I have already made a unit circle ..." so show that..(!) How are we to know where you are stuck? Commented Apr 2, 2018 at 13:51
• Closely related question. Commented Apr 2, 2018 at 15:58