difference in the sides of 2 regular decagons is equal to the circumradius
Source: Eotvos 1908 p3
September 8, 2024
geometrydecafoncircumcircle
Problem Statement
A regular polygon of 10 sides (a regular decagon) may be inscribed in a circle in the following two distinct ways: Divide the circumference into equal arcs and
(1) join each division point to the next by straight line segments,
(2) join each division point to the next but two by straight line segments. (See figures).
Prove that the difference in the side lengths of these two decagons is equal to the radius of their circumscribed circle.
https://cdn.artofproblemsolving.com/attachments/7/9/41c38d08f4f89e07852942a493df17eaaf7498.png