In the diagram, $AOB$ is a sector of a circle with $\angle AOB=60^\circ.$ $OY$ is drawn perpendicular to $AB$ and intersects $AB$ at $X.$ What is the length of $XY?$
Angle AOX = 30°
sin AOX = AX / AO
sin 30° AX / 20
20sin 30 = AX
20 (1/2) = AX = 10
OX = sqrt ( AO^2 - AX^2) = sqrt ( 20^2 - 10^2) = sqrt (300) = 10sqrt (3)
XY = OY - OX = 20 -10sqrt(3) = 10 ( 2 - sqrt (3) ) ≈ 2.679
