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Math Forum » Discussions » Math Topics » geometry.pre-college.independent

Topic: Six Circles Theorem
Replies: 4   Last Post: Dec 31, 1995 8:22 AM

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Mike de Villiers

Posts: 38
Registered: 12/6/04
Six Circles Theorem
Posted: Dec 28, 1995 4:32 PM
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Recently I came across the following interesting result in a Dutch math
journal. Does anyone have or know of a synthetic or transformation
geometry proof for this "six circles" theorem?
Triangle PQR is given. Circle A is drawn tangent to sides PQ and QR.
Circle B is tangent to Circle A and to the two sides QR and RP, Circle C
is tangent to Circle B and to sides RP and PQ, etc. Then the sixth circle
F is tangent to Circle A.

Michael de Villiers
Univ Durban-Westville
South Africa

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