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pow:problem3

Problem 3 (due Monday, March 16)

Recall that a $chord$ of a circle is a straight line segment whose endpoints both lie on the circle.

Several chords are drawn in a circle of radius 1 so that any diameter of the circle intersects at most $k$ of the chords. Prove that the sum of the lengths of all the chords drawn is less than $k\pi$.

Ashton Keith, a freshman majoring in math, is the only person who submitted a complete solution. His solution is very nice and different from our original solution. A solution along similar lines, but lacking sufficient details, was also submitted by Yuqiao Huang. Both our solution and the solution by Ashton Keith are discussed in the following link Solution

pow/problem3.txt · Last modified: 2020/03/19 01:33 by mazur