A geometry problem by Witchayut Jaroensattayathum

Geometry Level pending

ABC is a right triangle. O is the circumcircle of triangle ABC,I is the incircle of triangle ABC such that (AIO) ̂=2(CIO) ̂=90°. Therefore AB:BC:CA can be written as a:b:c where a,b,c are positive integers .Find the minimum value of a+b+c.

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