In the diagram, ABDF is a trapezoid with AF parallel to BD and AB perpendicular to BD. The circle with center B and radius AB meets BD at C and is tangent to DF at E. Suppose that x is equal to the area of the region inside quadrilateral ABEF but outside the circle, that y is equal to the area of the region inside △EBD but outside the circle, and that α=∠EBC. Prove that there is exactly one measure α, with 0∘≤α≤90∘, for which x=y and that this value of 21<sinα<21.[asy]
import graph; size(150); real lsf = 0.5; pen dp = linewidth(0.7) + fontsize(10); defaultpen(dp); pen ds = black; pen qqttff = rgb(0,0.2,1); pen fftttt = rgb(1,0.2,0.2);
draw(circle((6.04,2.8),1.78),qqttff); draw((6.02,4.58)--(6.04,2.8),fftttt); draw((6.02,4.58)--(6.98,4.56),fftttt); draw((6.04,2.8)--(8.13,2.88),fftttt); draw((6.98,4.56)--(8.13,2.88),fftttt);
dot((6.04,2.8),ds); label("B", (5.74,2.46), NE*lsf); dot((6.02,4.58),ds); label("A", (5.88,4.7), NE*lsf); dot((6.98,4.56),ds); label("F", (7.06,4.6), NE*lsf); dot((7.39,3.96),ds); label("E", (7.6,3.88), NE*lsf); dot((8.13,2.88),ds); label("D", (8.34,2.56), NE*lsf); dot((7.82,2.86),ds); label("C", (7.5,2.46), NE*lsf); clip((-4.3,-10.94)--(-4.3,6.3)--(16.18,6.3)--(16.18,-10.94)--cycle);
[/asy] geometrytrapezoidtrigonometrygeometry proposed