Locus?

Two sticks, of lengths $10$ and $20$ respectively, slide along the axes of a coordinate system such that one end of each stick slides along the $X$ -axis while the other end of each slides along the $Y$ -axis. The four end points of the sticks always lie on a circle. The locus of the centre of this circle can be expressed as $(ax-by) ^2+(bx-ay)^2=c^2$ , where $a, b$ and $c$ are coprime positive integers. Find the value of $a+b+c$ .

Inspiration