# Geometry/Trigonometry Puzzle

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 July 13, 2006, 17:30 Geometry/Trigonometry Puzzle #1 RW Guest   Posts: n/a Ladies and Gentlemen: In the course of my CFD work, I've come upon a problem which at first seems nearly trivial, but which, I'm embarassed to say, I haven't solved. Perhaps someone can help. - Consider two line segments of known length. - They are connected together, non-parallel, and the angle they form is known. - Now without disturbing their geometry, consider those two segments as two adjacent, connected chords of a circle. What is the radius of the circle which circumscribes the two segments as valid chords? Thanks in advance.

 July 13, 2006, 19:43 Re: Geometry/Trigonometry Puzzle #2 Adrin Gharakhani Guest   Posts: n/a if one side has length a and the second has length c, and the line connecting the two extremes (to make a triangle) has length b, then the radius R of the circle is R = a.b.c / (4.D) where D = sqrt( s.(s-a).(s-b).(s-c) ) and s = ( a + b + c ) /2 adrin

 July 17, 2006, 15:31 Re: Geometry/Trigonometry Puzzle #3 RW Guest   Posts: n/a Thank you for replying: In my problem, we don't know the length b. But we do know the angle, phi, that is formed by the vertex of the two line segments. Any ideas? Rich

 July 17, 2006, 15:36 Re: Geometry/Trigonometry Puzzle #4 pc Guest   Posts: n/a If you know the end points of the two line segments a and c, then you know the length b, regardless of the angle, do you not?

 July 17, 2006, 16:05 Re: Geometry/Trigonometry Puzzle #5 Adrin Gharakhani Guest   Posts: n/a The length c, for known lengths a and b, and the angle C between them is given by the law of cosines: c^2 = a^2 + b^2 - 2.a.b.Cos(C) adrin

 July 17, 2006, 17:46 Re: Geometry/Trigonometry Puzzle #6 RW Guest   Posts: n/a We don't know the endpoints. We only know the lengths of the two line segments and the included angle. Rich

 July 17, 2006, 17:47 Re: Geometry/Trigonometry Puzzle #7 RW Guest   Posts: n/a Ah, thanks!

 July 30, 2006, 10:14 Re:Trigonometry Puzzle #8 LaDy_mHiNe08 Guest   Posts: n/a i need trigonometry puzzles for my project in mathIV. . . please give me a trigonometry puzzles. . .

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