Three Equal Chords

Points $A,B,C,D$ lie in this order on a circle of radius $10$ so that $AB=BC=CD=10$. Find the area of quadrilateral $ABCD$. The answer is in the form $\frac{a\sqrt{b}}{c}$ for where $a$, $b$, $c$ are positive integers, $\gcd(a,c) = 1$, and $b$ is square-free. Input the answer as the sum $a+b+c$.