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anonymous

  • 5 years ago

Pleaaaase help me! What is the radius (r) of a circle inscribed in a "12-16-20" right triangle? The answer must be either a whole number, in reduced fraction form, or simplified radical form (no decimals). I can't paste the picture here but what it basically looks like is a right triangle with the two legs being 16 and 12 and the hypotenuse being 20. Inside the triangle is a circle and there is one radius line drwan in it...

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  1. amistre64
    • 5 years ago
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    if you connect the angles with the midpoint of the opposite sides, you find the center of the triangle.... that much I have so far :)

  2. anonymous
    • 5 years ago
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    What do you know about incentres/incircles? I guess nothing, as then this would be trivial :/

  3. amistre64
    • 5 years ago
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    I come to radius=4. If we take the intersection of the lines as the center for our circle, then y = 4... if I did it right :)

  4. anonymous
    • 5 years ago
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    You are right.. In general, the radius is (xy)/(x+y+z) - where z = hypotenuse.

  5. amistre64
    • 5 years ago
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    y = (3/8)x and y = -(3/4)x + 12 is what I used

  6. amistre64
    • 5 years ago
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    yay!!... im glad I was right :) thanx

  7. anonymous
    • 5 years ago
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    I like your method, by the way. I've seen others answer questions like that with lines rather than geometric rules, and it always surprises me - I never spot to do things like that :(

  8. amistre64
    • 5 years ago
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    x = 32/3 which when plugged in gets me y = 4 :)

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