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We consider two spheres. The sphere of radius 3 centered at the origin (0, 0, 0).  The second sphere is tangent to the first sphere and is centered at A(3, 5, 2). Find the point of intersection P of these spheres.

Hint: The points A, P and the origin are on the same line.

This means that the line of the forms 3Ax + 5Ay + 2Az contains both the centers.
This can be seen since At A=0, it contains (0,0,0) and at A=1, it contains (3,5,2).

The length along the line from A = 0 out to A = t is
is sqrt((3t) + (5t) + (2t)).

Since 3 squared, 5 squared, and 2 squared are, respectively, 9, 25, and 4,
and 9+25+4 = 38, this is the same as sqrt(38t).

The edge of the inside sphere is then at where the equation 38t = 3 is satisfied.
That is, t = 9/38, or  t = 3*sqrt(38)/38.  The point is (9,15,6)*sqrt(38)/38.
That gives the value (1.4600, 2.4333, 0.9733).

Since this is almost half the distance to the outside sphere,
the radius of the outside sphere would be a little bit bigger than the inside.

It would be roughly (1.5400 + 2.5667 + 1.0267), which is roughly 3.16.  

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Scott A Wilson


I can answer any question in general math, arithetic, discret math, algebra, box problems, geometry, filling a tank with water, trigonometry, pre-calculus, linear algebra, complex mathematics, probability, statistics, and most of anything else that relates to math. I can also say that I broke 5 minutes for a mile, which is over 12 mph, but is that relevant?


Experience in the area; I have tutored people in the above areas of mathematics for over two years in I have tutored people here and there in mathematics since before I received a BS degree back in 1984. In just two more years, I received an MS degree as well, but more on that later. I tutored at OSU in the math center for all six years I was there. Most students offering assistance were juniors, seniors, or graduate students. I was allowed to tutor as a freshman. I tutored at Mathnasium for well over a year. I worked at The Boeing Company for over 5 years. I received an MS degreee in Mathematics from Oregon State Univeristy. The classes I took were over 100 hours of upper division credits in mathematical courses such as calculus, statistics, probabilty, linear algrebra, powers, linear regression, matrices, and more. I graduated with honors in both my BS and MS degrees. Past/Present Clients: College Students at Oregon State University, various math people since college, over 7,500 people on the PC from the US and rest the world.

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Master of Science at OSU with high honors in mathematics. Bachelor of Science at OSU with high honors in mathematical sciences. This degree involved mathematics, statistics, and computer science. I also took sophmore level physics and chemistry while I was attending college. On the side I took raquetball, but that's still not relevant.

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