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# Analytic Geometry

Coordinates, mass points, and even some complex numbers.

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Points $$A, B,$$ and $$C$$ lie at $$(0,0), (3,0)$$, and $$(0,4)$$ respectively. What is the perimeter of $$\triangle ABC$$?

A circle contains points $$(0,4)$$ and $$(3,0)$$. What is the equation of the line which contains all possible centers of this circle?

Let $$ABC$$ be a triangle, and let $$D, E, F$$ be the midpoints of $$BC, AC, AB$$ respectively. Let $$G$$ be the intersection of $$AD, BE,$$ and $$CF$$. Find $$\frac{AG}{GD} + \frac{BG}{GE} + \frac{CG}{GF}$$.

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