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Math Help - FInd the incenter

  1. #1
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    FInd the incenter

    A triangle is located at A(-2,-5), B(0,7), and C(6,1)

    Find the incenter.

    I get the answer (4,3), but that's impossible. I'm stuck on this question for half an hour!

    Thanks.
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  2. #2
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    Quote Originally Posted by chengbin View Post
    A triangle is located at A(-2,-5), B(0,7), and C(6,1)

    Find the incenter.

    I get the answer (4,3), but that's impossible. I'm stuck on this question for half an hour!

    Thanks.

    please show your work

    my approach
    let incentre is at (x,y) , then it will be equidistant from A(-2,-5), B(0,7), and C(6,1)
    using distance formula
     (x+2)^2+(y+5)^2=(x-0)^2+(y-7)^2 ..........(1)
     (x+2)^2+(y+5)^2=(x-6)^2+(y-1)^2 ..........(2)
    solving (1)and (2),
    x+6y=5 and 4x+3y=2

    which gives

    x= \frac{-1}{7} and y= \frac{6}{7}
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  3. #3
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    Using the formula \frac {ax_1+bx_2+cx_3}{a+b+c}, \frac {ay_1+by_2+cy_3}{a+b+c}

    a=6\sqrt 2, b=10, c=2\sqrt {37}

    \frac {-12\sqrt 2 +12\sqrt {37}}{6\sqrt 2+10+2\sqrt {37}}, \frac{-30\sqrt 2+70+2\sqrt {37}} {6\sqrt 2+10+2\sqrt {37}}

    Oh I see my error, but I don't know how to get your answer with this formula.

    Actually, your answer is wrong too. Your knowledge of the incenter is incorrect.
    Last edited by chengbin; November 1st 2009 at 06:43 PM.
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  4. #4
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    Quote Originally Posted by ramiee2010 View Post
    please show your work

    my approach
    let incentre is at (x,y) , then it will be equidistant from A(-2,-5), B(0,7), and C(6,1)
    using distance formula
     (x+2)^2+(y+5)^2=(x-0)^2+(y-7)^2 ..........(1)
     (x+2)^2+(y+5)^2=(x-6)^2+(y-1)^2 ..........(2)
    solving (1)and (2),
    x+6y=5 and 4x+3y=2

    which gives

    x= \frac{-1}{7} and y= \frac{6}{7}
    equidistant from the 3 vertices???
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  5. #5
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    I got AB: y = 6x + 7 so its slope is +6
    AC: y = 0.75x + 0.25 so its slope is +0.75
    BC: y = -x + 7 so its slope is -1

    I am not sure but I believe the slope of AO = (AB + AC)/2 = 27/8
    then i am stuck at finding the slopes of BO, CO.
    with their slopes found and the coordinates of 3 vertices given, the equations of AO, BO, CO can be found? and then the common solution (x, y) to these three be found???
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