Professor McWorter sent me a one page paper he came across while rummaging through some old stuff. The paper appeared in Eureka, Vol. 2, no. 8, October, 1976, p. 162. It's reproduced below as accurately as possible. Two footnotes are either Bankoff's or the journal editor's. The second one is especially noteworthy.
But YM - ZL = QN; hence YC - ZB = QC. But YC - YQ = QC. Therefore YQ = ZB; and since PQ = PB, it follows that PZ = PY. Then, since X is the incenter of triangle BCP, PX bisects the angle BPC, and triangles XYP and PZX are congruent. So ZX = XY. Similarly, it can be shown that ZY = ZX = XY.
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This proof was communicated by the renowned problemist, Professor Euclide Paracelso Bombasto Umbigio, Guyazuela, to Dr. LEON BANKOFF, Los Angeles, California, who kindly translated it for us. The original proof was written in Esperanto, which Dr. Bankoff speaks like a native. Professor Umbigio is known primarily as a numerologist; this is one of his rare excursions in geometry.
YM/YC = ZL/ZB = QN/QC or (YM - ZL)/(YC - ZB) = QN/QC.
