Rotate a circle

[CaptainCrunch]

I have two congruent circles, side by side, touching at a single point. What I'd like to do is rotate the right hand circle 180 degrees about this point so that it ends up superimposed on the left hand one. I've tried making a circle from a point, and by entering an equation but when I select the point and the circle and right-click, there is no option to rotate in the menu.

Any help you can offer is appreciated.

[Support]

Hi Captain Crunch,

There are a few ways you could do this.

1. The first way is to select the circle you want to rotate, right-click and select Create Data Set. Select the Data Set and the point you want to rotate about, right-click and choose Rotation. The downside of this simple method is that our circle is replaced by a lot of points.

2. Another solution to use a bit of geometrical construction to give you control over the position of the circles. There are lots of ways to do this but here is one: http://screencast.com/t/MDbKhVIXYo

Hope that helps,

Simon

[CaptainCrunch]

Hi Simon,

I have revisited this construction and added to it by creating a chord on the dependent circle. When moving the point M around the left circle's circumference, the right circle appears to be rotating about M, but the chord acts like it's translating, in other words, like it's not rigidly connected to the circle. Is there anyway to lock the two together?

Thanks,
Eric

[Support]

Hi Eric,

There are a couple of ways to do this. Basically the points on the circle "don't know" that the circle is rotating about another circle. All they know is that the centre of the circle is changing and they change their positions accordingly.

Therefore what you need is to develop your construction so that the points on the circumference know that they need to rotate around the rotating circle as the circle rotates about the stationary circle.

There are a few different ways to do this, I have described one geometric and one graphical way in this video: http://screencast.com/t/7Gv33jpV9fPi

The very end of the video has been cut off because I am using Jing which limits to 5 minutes.

Hope that helps,

Simon