Maximizing with an Orthic Condition

Level 3

A triangle ABCABC with sidelengths a,b,ca,b,c and circumradius RR has the property that its medial triangle is congruent to its orthic triangle.

What is the minimum possible value of a2+b2+c2R2?\frac{a^2+b^2+c^2}{R^2}?

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