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Thread: Funny Geometry problem

  1. #1
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    Default Funny Geometry problem

    Imagine you got an acute-angled triangle ABC. At one side you put a point P, and then you draw right-angled lines like this:



    How can I construct P so that a triangle emerges?


    Allowed stuff: compass and ruler.
    Needed stuff: ruler, and something to do a right angle.

    Took me over 4 weeks to find it (yes I got it finally!), lets see if SRL can do it faster

    Edit: you also need to proove your solution. The prize: the fact that you did something you can't seem to find on Google

    Update: I'm going to give three hints, the same ones my maths teacher gave me: Highlight to view

    1. Look for similar triangles
    2. For the algebraic solution: ebook3000.com/Topics-in-Elementary-Geometry_24063.html, chapter 15 (A Closure Problem for Triangles)
    3. http://i48.tinypic.com/107qrrl.png
    Last edited by Markus; 01-11-2010 at 06:08 PM.
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    Default

    What do you mean by construct p.
    Oh Hai Dar

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    Well im not sure what your saying...
    erase the line, and redraw it? O_o
    explain further please
    NYAN NYAN NYAN NYAN NYAN NYAN NYAN NYAN NYAN NYAN NYAN NYAN NYAN

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    Quote Originally Posted by Main_Ftw View Post
    What do you mean by construct p.
    That you can pinpoint P exactly at a given triangle, so that a triangle like in the second pic appears.

    Quote Originally Posted by bionicle1800 View Post
    Well im not sure what your saying...
    erase the line, and redraw it? O_o
    explain further please
    Can't say it more detailed. Just take a look at the pics to see what I want
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    This could be done with Thales no ?

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    Quote Originally Posted by Dr D. Dervish View Post
    This could be done with Thales no ?
    Tried it but couldn't find out the right way to do it. But if you can find out how to do it, give it a shot!
    I made a new script, check it out!.

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    I have found the solution method and now Markus is forcing me to post, most likely to bump this up!
    By reading this signature you agree that mixster is superior to you in each and every way except the bad ways but including the really bad ways.

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    Quote Originally Posted by mixster View Post
    I have found the solution method and now Markus is forcing me to post, most likely to bump this up!
    My evil plan is discovered
    Last edited by Markus; 01-11-2010 at 07:11 PM.
    I made a new script, check it out!.

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    Are the triangles equilateral?
    Last edited by hubbard1989; 01-11-2010 at 08:42 PM.

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    Quote Originally Posted by hubbard1989 View Post
    Are the triangles equilateral?
    No, maybe in the pics it looks like one, but it can be any acute triangle.
    I made a new script, check it out!.

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    by equilateral did he mean all 3 outside triangles are congruent or just the middle being equilateral.

    My question is are all 3 of the outer triangles congruent and is the center triangle equilateral?

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