2002 AMC 12P Problems/Problem 24
Problem
Let be a regular tetrahedron and Let be a point inside the face Denote by the sum of the distances from to the faces and by the sum of the distances from to the edges Then equals
Solution
Assume points , , and are on faces , , and respectively such that , , and .
Assume points , , and are on edges , , and respectively such that , , and .
Consider triangles , , and . Each of these triangles have a right angle and an angle equal to the dihedral angle of the tetrahedron, so they are all similar by AA similarity. In particular, we know that .
See also
2002 AMC 12P (Problems • Answer Key • Resources) | |
Preceded by Problem 23 |
Followed by Problem 25 |
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