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## Main Question or Discussion Point

I have a sphere, with center x0,y0,z0 and a radius r.

Furthermore I have a point 1 outside the sphere x1,y1,z1.

But now I want to calculate the coordinates of Point 2, which is on the surface of the sphere, and the CenterP2P1 is 90 degrees there.

With these two points known points (Center & P1), I want to make a triangle.

Sides:

- Center - P1 (length calculated by Euclidean distance)

- Center - P2 (length = radius of the sphere)

- P1 - P2 (length = Pythagoras formula)

With Euclidean distances it is easy to calculate all the lengths of all the sides.

But can someone point me towards the possible very simple solution of this problem, how to calculate the coordinate of point 2?

Furthermore I have a point 1 outside the sphere x1,y1,z1.

But now I want to calculate the coordinates of Point 2, which is on the surface of the sphere, and the CenterP2P1 is 90 degrees there.

With these two points known points (Center & P1), I want to make a triangle.

Sides:

- Center - P1 (length calculated by Euclidean distance)

- Center - P2 (length = radius of the sphere)

- P1 - P2 (length = Pythagoras formula)

With Euclidean distances it is easy to calculate all the lengths of all the sides.

But can someone point me towards the possible very simple solution of this problem, how to calculate the coordinate of point 2?