From: grossman@vela.acs.oakland.edu (Jerry Grossman) Newsgroups: sci.math,k12.ed.math Subject: Re: geometry problem Date: 31 Aug 1995 12:14:30 -0400 This message is being posted by Jerry Grossman for its writer, Tony Davie, whose system wasn't working. It's in response to the following geometry problem that Grossman posted: >This is a classic geometry problem, which I am embarrassed to say I can't >see how to do. Can someone help out? A "correct" solution must use only >elementary geometry, no trigonometry. There was an article within the >past year on this problem and related ones, but I can't seem to find it. >Does anyone recall where it appeared? (Other references are also >appreciated.) > >ABC is a triangle. D is a point on AB, and E is a point on AC. Angle >measures (in degrees) are as follows: >EBC = 60 ABE = 20 BCD = 70 ACD = 10 >Find the measure of angle CDE. This is a special case of what have become known as Adventitious angles (or triangles or quadrangles). I have collected a small bibliography on the subject which I show below. If you can surf the Web, I've written a small page on the problem at http://www.dcs.st-and.ac.uk/~ad/mathrecs/advent/advent.html Here's the bibliography: [lang22] A Problem: E.M. Langley, Mathematical Note 644, Mathematical Gazette, 11, p173, 1922 [lang23] Solutions: E.M. Langley et al., Mathematical Gazette, 11, pp321-323, 1923 [bol36] Beantwoording van prijsvraag no. 17: Nieuw Archf Wisk. (2) 18, pp14-66, 1936 [trip75] Adventitious Angles: C.E. Tripp, Mathematical Gazette, 59, pp98-106, 1975 [quad77] The Adventitious Angles Problem: A Progress Report: D.A. Quadling, Mathematical Gazette, 61, pp55-58, 1977 [rigb78] Adventitious Quadrangles: J.F. Rigby, Mathematical Gazette, 62, pp183-191, 1978 [rigb79?] Multiple Intersections of Diagonals of Regular Polygons, and Related Topics: J.F. Rigby, Geom. Dedicata, later than [rigb78] [quad78] Last Words on Adventitious Angles: D.A. Quadling, Mathematical Gazette, 62, pp174-183, 1978 [mach95] Nineteen Problems on Elementary Geometry: A. Machado, Math. Intelligencer, 17, 1, pp17-19, 1995 [gale95] Mathematical Entertainments: D. Gale, Math. Intelligencer, 17, 1, pp21-26, 1995 [Davie's sig deleted - djr] ==============================================================================