Hint, there is something wrong with the graphic letters in the supplementary question, and the positions of A and D should be reversed.

(1) link OE

Because CD is tangent to o and e,

So OE vertical CD

And because AB= 10.

So OE=5.

(2) If A is AF, the vertical CD is in F,

Because the quadrilateral ABCD is a parallelogram, OE is perpendicular to CD.

So OA=OE=EF=AF=5,

Because ∠ ABC = 60

So ADC = 60.

In the RT triangle, ∠ ADC = 60, ∠ AFD = 90,

So DF=5/3 times√ 3.

That is, DE=5+5/3 times √3.

S shadow = S trapezoid AOED-S fan OAE=25/4+5/6 times √3.