Circles With No Intersects Outside Each Other, Point Lies Outside Both Circles

Number of solutions: 4

SOLUTION METHOD

Circle inversion

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Steps

1. Draw a circle centered at point A and proceed with a circle inversion.
2. Invert all objects in the problem through the circle inversion from step 1. This leaves point A at infinity.
3. Draw the common tangents of the circles. They meet the point at infinity.
4. We invert the tangents from step 3 through circle inversion from step 1.
5. 4 solutions arise.

SOLUTION METHOD

Loci of points satisfying certain properties

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Steps

1. Chybí postup