When a point inside of a tetrahedron (a solid with four triangular surfaces)…
2014
When a point inside of a tetrahedron (a solid with four triangular surfaces) is connected by straight lines to its corners, how many (new) internal planes are created with these lines? _____________
Attempted by 33 students.
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Correct answer: 6
Answer: 6
Explanation: Each internal plane is determined by the interior point together with two of the tetrahedron's vertices (three noncollinear points determine a plane).
Count the pairs of vertices: there are 4 vertices, so the number of distinct pairs is 4 choose 2 = 6.
Each pair of vertices together with the interior point gives a unique plane (these planes are different because the tetrahedron's vertices are not coplanar with the interior point), so there are 6 internal planes in total.