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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 

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 

Good luck and take care.

-Doctor Chaos,  The Math Forum
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Associated Topics:
High School Euclidean/Plane Geometry
High School Geometry
High School Logic
Middle School Geometry
Middle School Logic
Middle School Two-Dimensional Geometry
Middle School Word Problems

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