Is Henry Guilty? (Geometry Puzzle)
Date: 6/10/96 at 21:7:6 From: Anonymous Subject: Geometry (puzzle) In Hughmoar County, residents shall be allowed to build a straight road between two homes as long as the new road is not perpendicular to any existing county road. Penalty for breaking this is to "per pendere". Warren Peese (A: Army General,) Howie Gettindere (B: Locksmith), and Ann Teek (C: Oldest Settler) lived at the intersections of three straight dirt roads which formed an equilateral triangle of side length 9 miles. Now, Tim Burr (D: Lumberjack) eventually built a house on the road between Warren Peese and Ann Teek such that Tim Burr lives 3 miles from Warren Peese. Earl Lee Byrd (E: Bait Shop Supplier) built a house on the road between Howie Gettindere and Ann Teek. Two new straight roads soon were built, one between Howie Gettindere and Tim Burr and the other between Warren Peese and Earl Lee Byrd, which surprisingly met at one location in a heavily wooded area, the hidden residence of Henry Mover (F: Chicken Thief). Since his hiding place had been exposed, Henry Mover decided to become honest and built a special straight road which connected his home to that of Ann Teek. However, on the completion of the road, Henry Mover was promptly arrested by Cher Eff (G: County Constable) and charged with breaking LAW #98. Is Henry Mover guilty? Prove your case using the evidence provided. (NOTE: Draw a picture using the letters suggested.) Well, there it is! I have the picture drawn, and I suspect that Henry is guilty. I'm stuck though, when it comes to proving why. :( Please Help. Thanks a lot, Tyler Stevens
Date: 6/18/96 at 13:38:19 From: Doctor Chaos Subject: Re: Geometry (puzzle) Hi Tyler. Henry is guilty only under 2 conditions, according to what you've given us. According to your description, we don't really know where point E (Earl Lee Bird) has built. If point E is 3 miles from Point C, then YES Angle DFC is 90 degrees. But also if Point E is closer to point B, then angle EFC becomes 90 degrees. This is not as easy to determine. I'll just say that it's much closer to point B than point C. Can YOU figure out where it should go? Let me know what you discover. Good luck and take care. -Doctor Chaos, The Math Forum Check out our web site! http://mathforum.org/dr.math/
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