There are three circles on the plane, circle a, circle b and circle C.

The intersection of the tangents of circle a and circle b is p;

The intersection of the tangents of circle b and circle c is q;

The intersection of the tangents of circle a and circle c is r;

Then, the PQR three-point line * * *.

If we use plane geometry knowledge, this theorem is more difficult to prove.

But if you put the "auxiliary line" in the space, it seems to be understood in an instant!

Prove:

We consider three balls, ball A, ball B and ball C.

The centers of these three balls are on the plane S.

The intersection of two tangent planes u and v of three balls is on a straight line T.

Then because the symmetry t is on the plane s,

Let's consider the cone formed by the tangents of two balls. Get three vertices of the cone.

The vertex of any cone can be determined by the common tangent of two balls in u and v.

So you should understand now that the vertices of the three cones are PQR, and the straight line T is the straight line where PQR is located.