Consider an isosceles trapezoid and two circumferences as illustrated in the figure below. Find the length of segment AB that connects the centers of the circles.
Attemp: Height is 3.6, therefore radius is 1.8 Consider the circle with center A. Draw the radius that are perpendicular to the 4.5 side and the 18 side and draw the segment from the center the lower left vertex. Consider the right triangle formed by that segment, the 18 side, and the radius. The angle closest to the lowerleft vertex is half that of a 3-4-5 triangle. Using tan half angle formula, we get that the tan of this angle is 1/2. Since this right triangle has one leg of 1.8 (the radius), its other leg is 3.6. So the length of AB is 18-2*3.6=10.8
Correct?
Here is quicker way to compute the segment length AB = $x$. With $a+b = 4.5$, establish the equation below for the perimeter $p$,
$$ p= 2x + 4(a+b) = 2x+18=12.6+18+9$$