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Question: 3D Plot - Intersection of Plane with Sphere and Tetraeder

Given is a sphere and a tetraeder. How can I (calculate and) plot the intersection of a plane with both objects? The intersection shoud be a circle and a triangle (in 2D or 3D). I tried a lot, but it didn't work out at all. The intersection command just works e.g. with two spheres. Many thanks for any help in advance!
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