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Javascript Version

Area of the Triangle Formed by the Intersection of Common Tangents to 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.

Can you infer the relationship between this ratio and the radii of the circles?

If you are interested in this applet, you may like our Interactive Symbolic Geometry software Geometry Expressions.