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Math Help - circle

  1. #1
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    circle

    Sorry >__<

    I need help on this question

    There is a circle inscribed in a triangle.

    so if AB=12, BC=16, and AC= 20, <B=90...then what is the radius of the inscribed circle?

    I dunno how to draw a picture here.......but the diagram should be a scalene triangle with a circle inscribed inside it.
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  2. #2
    Senior Member tukeywilliams's Avatar
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    I believe the radius is the following:

     r = \frac{\sqrt{k(k-a)(k-b)(k-c)}}{k} (Herons Formula) where  k = \frac{1}{2}(a+b+c) .

    So  k = \frac{1}{2}(20 + 16 + 12) = 24 .

    And  r =  \frac{\sqrt{24(24-20)(24-16)(24-12)}}{24} = 4
    Attached Thumbnails Attached Thumbnails circle-pic.jpg  
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  3. #3
    Math Engineering Student
    Krizalid's Avatar
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    Use Poncelet's Theorem

    12+16=20+2r\implies{r}=4
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  4. #4
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    Hello, charrie berri!

    There is a circle inscribed in triangle ABC.

    If AB=12,\;BC=16,\;AC= 20,\;\angle B = 90^o
    . . what is the radius of the inscribed circle?
    The radius r of the inscribed circle can be found with: . A \;=\;\frac{1}{2}pr
    . . where: . \begin{array}{ccc} p & = & \text{perimeter} \\ r & = &\text{radius} \\ A & = & \text{area} \end{array}


    The perimeter is: . p \:=\:12 + 16 + 20 \:=\:48

    The area is: . A \:=\:\frac{1}{2}(12)(16) \:=\:96 .
    . . . It's a right triangle!

    So we have: . 96 \:=\:\frac{1}{2}(48)r\quad\Rightarrow\quad\boxed{r \,=\,4}

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  5. #5
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    THANK YOU!!! I REALLY APPRECIATE IT.

    And I need help on one last question........

    In Circle O, <OAB=24 and <OCB= 60. What is the measure of <ABC.....


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