Dancing Rods

Geometry Level 3

Let two Rods ABAB of length 1010 and CDCD of length 2020 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,DA,B,C,D is expressed as:

(axby)2+(bxay)2=c2 (ax-by)^2 + (bx-ay)^2 = c^2

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

Details and Assumptions

  • Diagram not up to scale
Inspired from Kushal Patankar's Problem

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