When a point inside a tetrahedron is connected by straight lines to its corners, how many new internal planes are created by these lines?

Correct answer: 4

Solution

A tetrahedron has 4 triangular faces. Connecting an interior point to all four vertices divides the solid into 4 smaller tetrahedra, corresponding to 4 internal planes/regions in the intended spatial-aptitude sense. Hence the answer is 4.

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