2008 UNCO Math Contest II Problems/Problem 6
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 ?
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, .
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