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Thread: [SOLVED] isosceles trapezoid

  1. January 24th 2010, 03:34 PM #1
    Garas
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    [SOLVED] isosceles trapezoid

    How to prove that diameter of the circle within isosceles trapezoid is a geometric mean of bases?
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  2. January 24th 2010, 11:10 PM #2
    earboth
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    Quote Originally Posted by Garas View Post
    How to prove that diameter of the circle within isosceles trapezoid is a geometric mean of bases?
    You are dealing with 2 similar right triangles.

    Use proportions:

    \dfrac{\frac c2}{r} = \dfrac{r}{\frac a2}~\implies~a\cdot c = 4r^2

    Calculate the square-root at both sides which yields the given result.
    Attached Thumbnails Attached Thumbnails [SOLVED] isosceles trapezoid-glschklgtrapez_inkreis.png  
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