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Math Help - Geometry Puzzle

  1. #1
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    Question I really need a hint or a solution

    Problem:
    There is a point A with an angle. Let there be a point P in the angle. Make a line from B to C through P to give the triangle ABC minimum area.
    [HTML]
    /C
    /
    /
    / * P
    /
    A -------------B

    Please.. make my day.[/HTML]
    Last edited by musamba; May 30th 2005 at 12:06 PM.
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  2. #2
    Site Founder MathGuru's Avatar
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    Smile

    The area ABC seems to be predetermined.
    Why does it matter where P is placed? there is only one possible line that goes through C and B.

    Please try to give some more information
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  3. #3
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    It doesn't matter where point P is placed. The difficult part about the problem is to draw a line to make the area smallest.
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  4. #4
    Site Founder MathGuru's Avatar
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    But are point C and B already determined? If you can't move them there is only one possible line you can draw between them. I think I am missing something here.

    Remember a line is the shortest possible distance between two points so unless we can move the two points in the line we can't really minimize the area.

    Maybe if you give me some background for the question. Is this for school or is it for something else. What have you been studying recently that this question might be testing?
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  5. #5
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    No, that is exactly it. Point C and B are not determined.
    The question is a geometry puzzle i came over, but i never found the solution and it is really stealing my sleep.
    The question is not qurriculum based. The puzzles i came over can be solved by high school math.
    I'm in my last year before starting of in college in autumn.
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  6. #6
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    Okay

    Why not make the angle between AB and AC very very small, even infinitaley small. Are there any other constraints to the problem?

    Have you reproduced the problem in its entirety here?
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  7. #7
    hpe
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    Quote Originally Posted by musamba
    No, that is exactly it. Point C and B are not determined.
    The question is a geometry puzzle i came over, but i never found the solution and it is really stealing my sleep.
    The question is not qurriculum based. The puzzles i came over can be solved by high school math.
    I'm in my last year before starting of in college in autumn.
    Make the triangle isosceles (i.e. B and C should have the same distance from A). There is a Calculus proof that this is minimal.
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