Mock AIME 1 Pre 2005 Problems/Problem 3
Problem
and are collinear in that order such that and . If can be any point in space, what is the smallest possible value of ?
Solution
Let the altitude from onto at have lengths and . It is clear that, for a given value, , , , , and are all minimized when . So is on , and therefore, . Thus, =r, , , , and Squaring each of these gives:
This reaches its minimum at , at which point the sum of the squares of the distances is .
See also
Mock AIME 1 Pre 2005 (Problems, Source) | ||
Preceded by Problem 2 |
Followed by Problem 4 | |
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 |