# [SOLVED] isosceles trapezoid

• Jan 24th 2010, 04:34 PM
Garas
[SOLVED] isosceles trapezoid
How to prove that diameter of the circle within isosceles trapezoid is a geometric mean of bases?
• Jan 25th 2010, 12:10 AM
earboth
Quote:

Originally Posted by Garas
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.