Crux’s crux’s crux
Sasane, A.
(2022).
Crux’s crux’s crux.
Mathematics Magazine,
95(5), 458 - 464.
https://doi.org/10.1080/0025570X.2022.2126264
(2022).
Crux’s crux’s crux.
Mathematics Magazine,
95(5), 458 - 464.
https://doi.org/10.1080/0025570X.2022.2126264
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.