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Maximum and the minimum of the sum of the lengths [ILL 1977]

Source:

January 11, 2011
calculusgeometry unsolvedgeometry

Problem Statement

Two perpendicular chords are drawn through a given interior point PP of a circle with radius R.R. Determine, with proof, the maximum and the minimum of the sum of the lengths of these two chords if the distance from PP to the center of the circle is kR.kR.