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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