1999 AHSME Problem 21

A circle is circumscribed about a triangle with sides 20,21, and 29, thus dividing the interior of the circle into four regions. Let A,B, and C be the areas of the non-triangular regions, with C be the largest. Then

\mathrm{(A) \ }A+B=C \qquad \mathrm{(B) \ }A+B+210=C \qquad \mathrm{(C) \ }A^2+B^2=C^2 \qquad \mathrm{(D) \ }20A+21B=29C \qquad \mathrm{(E) \ } \frac 1{A^2}+\frac 1{B^2}= \frac 1{C^2}

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.