2008 UNCO Math Contest II Problems/Problem 6
Problem
Points and are on the same side of line in the plane. is units away from is units away from . The distance between and is . For all points on what is the smallest value of the sum of the distances from to and from to ?
Solution
Construct , the reflection of across , and , the foot of the perpendicular from to the segment connecting to . By Pythagorean Theorem, . The minimum possible value of is equal to the minimum value of , which is equal to the length of . By Pythagorean Theorem, .
See Also
2008 UNCO Math Contest II (Problems • Answer Key • Resources) | ||
Preceded by Problem 5 |
Followed by Problem 7 | |
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 | ||
All UNCO Math Contest Problems and Solutions |