Proposed by Bill Livingston, Missouri Southern State University. The product of three real numbers is
-1/2 and the sum of their squares is 57/4. If the three numbers are taken two at a time and multiplied,
the sum of the reciprocals of these products is -7. Determine these three numbers.
Proposed by Efim I. Cherkassy, Rasba Institute, Israel, and Alexander A. Katz, St. John's University, NY.
In a triangle ABC, AB is perpendicular to AC and the incircle touches BC at D. Prove that the area of ABC
is equal to the product of BD and CD.
Proposed by U. I. Lydna, Beloretsk, Russia. In triangle ABC, BC^2 = AB(AB+AC). Prove that angle A is twice angle
C without using trigonometry.
Proposed by Jerry Slocum, Beverly Hills. I had a set of seven tables arranged to form a square as in the standard
Tangram puzzle depicted in the diagram on the left (see Math Horizons). One day, I found my tables rearranged to
form a square with one-ninth of it missing, as depicted in the diagram on the right. At first, I thought someone
had stolen the small square table, until I realized that the proportions were wrong. In fact, all seven tables
were there. How were they arranged?