# Area of the Triangle Formed by the

Intersection of the Tangents of 3 Circles

It is a well known theorem that the exterior common tangents to 3 circles
intersect on a line.

The intersections of the interior common tangents
form the triangle PQR.

We see by dragging A B and C that the ratio of
the areas of PQR and ABC are
independent of the triangle ABC formed by the
centers of the circles, but depend
only on the radii of the circles.