References 1. S. A. Cook, The complexity of theorem-proving procedures, in Proceedings of the Third Annual ACM Symposium on the Theory of Computing. Eds. M. A. Harrison, R. B. Banerji, J. D. Ullman. Association for Computing Machinery, New York, 1971. 151–158. 2. M. Garey, D. S. Johnson, Computers and Intractability: A Guide to the Theory of NP-Completeness. Freeman, San Francisco, 1979. 3. R. M. Karp, Reducibility among combinatorial problems, in Complexity of Computer Computations. Eds. R. E. Miller, J. W. Thatcher. Plenum, New York, 1972. 85–103.

Proof Without Words: A Right Triangle Identity Roger B. Nelsen ([email protected]), Lewis & Clark College, Portland, OR Theorem. Let s, r, R denote that semiperimeter, inradius, and circumradius, respectively, of a triangle. For a right triangle, s = r + 2R. Proof. r

r

r

r

x

y

r y

x 2R

Moreover, since s > r + 2R for acute triangles and s < r + 2R for obtuse triangles, s = r + 2R characterizes right triangles [1]. Summary. We use a figure to relate the semiperimeter, inradius, and circumradius of a right triangle.

Reference 1. W. J. Blundon, On certain polynomials associated with the triangle, Math. Mag. 36 (1963) 247–248, http://dx.doi.org/10.2307/2687913. http://dx.doi.org/10.4169/college.math.j.47.5.355 MSC: 51N05

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