Incentre as MID point of centroid and orthocentre

Geometry Level 5

If incenter is midpoint of centroid and orthocenter for a triangle A B C ABC .
Find the minimum 9 a b + 9 b c + 9 c a a 2 + b 2 + c 2 \frac{9ab+9bc+9ca}{a^2+b^2+c^2} over all such triangles A B C ABC .


The answer is 8.

Mehul Kumar by Mehul Kumar , 23, India

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