A pentagon inscribed in a circle has equal angles. Show that it has equal sides.
Solution
Consider triangles ABC and DCB. We have ∠ABC = ∠DCB, BC = CB, ∠BAC = ∠CDB (because the pentagon is cyclic). Hence AB = DC. Similarly, AB = DE, BC = ED and BC = EA. So all sides are equal.
© John Scholes
jscholes@kalva.demon.co.uk
29 Oct 2003
Last corrected/updated 29 Oct 03