# Tangent Lines to a Ball From a Single Point

Geometry Level 4

Three lines pass through the origin, and are along the vectors $$(1, 2, 5) , (-1, 2, 3),$$ and $$(-2, -2, 3)$$.

A ball of radius 10 units is above these three lines, and tangent to all three of them.

If the center of the sphere is $$(a, b, c)$$, what is the value of $$a + b + c$$?

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