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**Touching three Circles**

How to find the red circle? The problem is due to Apollonius
of Perge as many other problems and results too. It was treated and solved by
Newton. The solution given here uses reflection at a circle.

Click with the right mouse button, and unhide all hidden
objects.

- First the black circles are enlarged, such that two of
them touch. You get the green circles.
- Then the all green circles are reflected at the blue
circle. We get two brown lines and a brown circle.
- By elementary constructions, we construct a red circle,
touching all brown objects.
- Reflecting that circle once more and enlarging it
yields the solution.

Here
is a similar construction.

### Technical Information

Most steps are completely hidden.