Correct solutions were also submitted by Tracy Thatcher, Ray Kremer.  From outside Bradley Univerisity, correct solutions were submitted by Al Zimmermann, Brian Laughlin, Patrick Maxfield, Burkart Venzke, Monty Gray, Tim Kelley, Bill Webb, Lorenzo Pozzoli, Emanuele Macri, Massimo Brignone, Bill Soudirette, Aaron David Kahn, Philippe Fondanaiche.

There are various sets of triangles which yield a solution to this problem.  Using the ones on the left you first solve for y by Pythagoras in the lower right triangle, substitute into the triangle on the upper left and use Pythagoras a second time.  The result is that the radius c of the upper log is Ö5 - 1.

The general case requires no additional strain, beyond a strong stomach for algebra.

Note that the right angle of the triangle on the upper left is not, in general, at the point of tangency of the two circles. Neither is it the case that the hypotenuses of the right triangles are generally parallel.
 

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Page last updated 14 February 2000.

ã2000 Alberto L. Delgado