Crux’s crux’s crux

Summary: A result of Archimedes states that for perpendicular chords passing through a point P in the interior of the unit circle, the sum of the squares of the lengths of the chord segments from P to the circle is equal to 4. A generalization of this result to (Formula presented.) chords is given. This is done in the backdrop of revisiting Problem 1325 from Crux Mathematicorum, for which a new solution is presented.