# Dancing Rods

Geometry Level 5

Let two Rods $$AB$$ of length $$10$$ and $$CD$$ of length $$20$$ are sliding on smooth standard co-ordinate axis such that their ends are always con-cyclic. If the locus of centre of that circle which pass through all four points $$A,B,C,D$$ is expressed as:

$(ax-by)^2 + (bx-ay)^2 = c^2$

For positive integers $$a,b,c$$. What is the minimum value of $$a+b+c$$

Details and Assumptions

• Diagram not up to scale
×