# How Well Do You Know Your Geometry?

Geometry Level 2

How many triangles $$ABC$$ are there with integer side lengths such that the area of the triangle formed by joining the orthocenter, the circumcenter and the centroid of $$\triangle ABC$$ is $$44$$ square units?

Details and assumptions:

The orthocenter of $$ABC$$ is the point at which the altitudes of $$ABC$$ intersect.

The circumcenter of $$ABC$$ is the point which is equidistant from $$A$$, $$B$$ and $$C$$.

The centroid of $$ABC$$ is the point at which the medians of $$ABC$$ intersect.

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