# Revisiting coordinate 3!

Geometry Level 4

A triangle $$ABC$$ is given where vertex $$A$$ is $$(1,1)$$ and its orthocenter is $$(2,4)$$.

Also sides $$AB$$ and $$BC$$ are members of the family of lines a$$x+by+c = 0$$, where $$a,b$$ and $$c$$ form an arithmetic progression.

If the coordinates of the circumcenter of the triangle $$ABC$$ can be represented as $$(d,e)$$, where $$d$$ and $$e$$ are real numbers, find $$d+e$$.

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