A regular 7-gon inscribed in a circle (ABCDEFG), with some other point H on the circle, in the arc CD. Show that the length sum of the blue chords equals the length sum of the green chords.

Solution

Please find here a solution using complex numbers.

A regular 7-gon inscribed in a circle (ABCDEFG), with some other point H on the circle, in the arc CD. Show that the length sum of the blue chords equals the length sum of the green chords. https://t.co/0aS6Ikwg5r By @MarshallWBuck pic.twitter.com/amJuNbB9WF

— Mirangu (@Mirangu1) November 16, 2023