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Thread: Triangle Construction

  1. #1
    Junior Member
    Joined
    Apr 2008
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    Triangle Construction

    Does anyone have an algorithm for constructing a triangle given one side, AB, and altitudes h and k from A and B respectively? (Using straightedge compass construction)
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  2. #2
    Super Member

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    Lexington, MA (USA)
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    Hello, GoldendoodleMom!

    Find an algorithm for constructing a triangle given one side, $\displaystyle AB$,
    and altitudes $\displaystyle h$ and $\displaystyle k$ from $\displaystyle A$ and $\displaystyle B$ respectively.
    (Using straightedge-compass construction)

    Draw line segment $\displaystyle AB.$
    Locate its midpoint $\displaystyle M.$
    Draw a semicircle with diameter $\displaystyle AB.$
    Code:
                  * * *
              *           *
            *               *
           *                 *
    
          *                   *
        A * - - - - * - - - - * B
                    M

    With $\displaystyle A$ as center and radius $\displaystyle h$, swing an arc cutting the semicircle at $\displaystyle P.$

    With $\displaystyle B$ as center and radius $\displaystyle k$, swing an arc cutting the semicircle at $\displaystyle Q.$

    Code:
                  Q
                  ∆ * *     P
              *     ∆     o
            *         ∆     *
           *       o    ∆    *
                o         ∆
          *  o              ∆ *
        A o - - - - * - - - - ∆ B
                    M

    Draw $\displaystyle AQ$ and $\displaystyle BP$, extending them to meet at $\displaystyle C.$

    The required triangle is $\displaystyle \Delta ABC.$

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  3. #3
    Newbie
    Joined
    Feb 2009
    Posts
    1

    Triangle Construction

    Hello
    For the past few days, I've been searching on the Internet for a triangle construction from its orthocenter, circumcenter and incenter. Unfortunately,I didn't find anything. Does anyone know something about this construction?
    Thank you.
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