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Math Help - sss or sas ?

  1. #1
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    sss or sas ?

    In the triangle ABC AC = BC = 20 inches and AB = 10 inches. Circle is inscribed in the triangle, what is the radius of the circle...see attached...#71
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    Where are you stuck?
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    well i'm pretty sure the one radius pointing down is the midpoint of AB so those 2 segments are 5 inches, then i bisected the 3 angles in the circle to figure out that Ar and Br should be 5 inches each. i dont know what to do next
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    Quote Originally Posted by igottaquestion View Post
    In the triangle ABC AC = BC = 20 inches and AB = 10 inches. Circle is inscribed in the triangle, what is the radius of the circle...see attached...#71
    sketch lines from each vertex to the incenter.

    note that the area of the three triangles formed sums to the area of the large triangle ...

    \frac{1}{2}(20)r + \frac{1}{2}(20)r + \frac{1}{2}(10)r = \frac{1}{2}(10)h

    25r = 5h

    r = \frac{h}{5}

    find the height of the triangle from the vertex angle to the base and you can find r
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    ok so the height is 5 sq rt of 15, so r=sq rt of 15?
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    That's it!
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  7. #7
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    Well...let equal sides = a and base = b

    radius incircle = bSQRT(4a^2 - b^2) / [2(2a + b)]

    OR (if you prefer the SQRT in denominator!):

    radius incircle = b(2a - b) / [2SQRT(4a^2 - b^2)]

    No need to calculate height.
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  8. #8
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    Quote Originally Posted by igottaquestion View Post
    In the triangle ABC AC = BC = 20 inches and AB = 10 inches. Circle is inscribed in the triangle, what is the radius of the circle...see attached...#71
    1. You are dealing with 2 right triangles. (see attachment)

    2. Grey triangle: h^2 + 5^2 = 20^2

    3. The right triangle at the top of the grey triangle:

    r^2+15^2 = (h-r)^2

    4. Calculate h from 2. and plug in this term into the equation in 3. Solve for r.

    Spoiler:
    You should come out with r = \sqrt{15}


    Second attempt: The 2 right triangles are similar. So use proportions:

    \dfrac r{15} = \dfrac5h

    First calculate h, then r using the proportion.
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