Question 26

Let $$ABC$$ be a triangle, $$D$$ be the midpoint of side $$BC$$, $$O$$ be the circumcenter and $$H$$ be the orthocenter. If the triangle $$ODH$$ is equilateral with side length equal to $$6$$ and the area of the triangle $$ABC$$ can be written as $$a\sqrt{b}$$, where $$a, b$$ are positive integers and $$b$$ is not divisible by the square of any prime, find $$a+ b$$.


Correct Answer: 92

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