Quadrilateral ABCD is an isosceles trapezoid, with bases AB and CD. A circle is inscribed in the trapezoid, as shown below. (In other words, the circle is tangent to all the sides of the trapezoid.) The length of the base AB is 2x, and the length of the base CD is 2y. Prove that the radius of the inscribed circle is sqrt(xy).
r = sqrt( x*y ) or r2 = x*y x < r < y
r = 2 x = 1.25 y = r2 / x y = 3.2
Important: AD = BC = x + y
Proof: sqrt [( y-x )2 + ( 2r )2 ] = x + y
4.45 = 4.45
This is one way to prove it.