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Math Help - Circumcenter of a triangle

  1. #1
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    Joined
    Jan 2010
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    Unhappy Circumcenter of a triangle

    I give up. I've tried different ways and to no avail, can someone please check my work, tell me where I went wrong and point me to the right direction?

    Coordinates X- (3,36)
    Y- (66, 69)
    Z- (97, 74)

    P midpoint of ZY,

    P 97 + 66 , 74 + 69
    2 2



    P 163 , 143
    2 2




    P ( 81.5 , 71.5 )

    Q- midpoint of XZ,



    Q 3 + 97 , 36 + 74
    2 2



    Q 100 , 110
    2 2



    Q (50 , 55)




    R midpoint of XY,



    R 3 + 66 , 36 + 69
    2 2

    R 69 , 105
    2 2




    R (34.5 , 52.5)



    Equation of line YR-
    Y=mx + b

    Y= 0.344x + b (97, 74)


    Slope of line YR-

    0.344

    52.5 74 = -21.5 =
    34.5 97 = -62.5 =


    74 = 0.344 (97) + b

    74 = 33.368 + b

    b = 74 33.368



    b = 40.632




    Equation of line YR-



    Y= 0.344x + 40.632

    Slope of line YQ-

    0.875

    55 69 = -14 =
    50 66 = -16 =


    Equation of line YQ-
    Y= 0.875x + b (66, 69)

    69 = 0.875 (66) + b

    69 = 57.75 + b

    b = 69 57.75



    b = 11.25

    Equation of line YQ-

    Y= 0.875x + 11.25

    Equation of line XP-
    Y = 0.452x + b ( 3, 36 )

    Slope of line XP-
    0.452




    71.5 36 = 35.5 =
    81.5 3 = 78.5 =

    36 = 0.452 (3) + b

    36 = 1.356 + b

    b = 36 -1.356



    b = 34.644

    Equation of line XP-

    Y= 0.452x + 34.644


    -y + (-0.875x) = -11.25
    y 0.452x = 34.644



    0.423x = 23.394
    0.423 = 0.423



    X= 55.305

    Y 0.452 (55.305) = 34.644

    Y 24.998 = 34.644



    Y = 59.642

    Point B (55.305 , 59.642)

    The coordinates of the circumcenter in triangle XYZ are (55.305, 59.642)
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  2. #2
    Member integral's Avatar
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    I always mess up these posts... (I'm a bad helper) Sorry...
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  3. #3
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    Quote Originally Posted by integral View Post
    if you know the coordinates just plug it into the Pythagorean theorem and find the lengths of each side (I am assuming by circumstance you mean perimeter... I have never heard it called anything other)

    c= \sqrt{a^2+b^2}
    I don't know what you mean by perimeter but circumcenter is the intersection of the 3 perpendicular bisectors in a triangle.
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  4. #4
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    It's alright integral, you tried.

    I tried a new method;
    -63/33 (34.5, 52.5)
    y - 52.5 = -1.909(x - 34.5)
    y - 52.5 = -1.909x + 65.861
    y = -1.909x + 118.361
    -.161 ( 81.5 , 71.5)
    y - 71.5 = -.161(x - 71.5)
    y - 71.5 = -.161x + 11.512
    y = -.161x + 83.012


    Is anything correct, at all?

    I got weird coordinates, please someone give me a step by step?
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