MathDB
Regular dodecagon

Source: Dutch Mathematical Olympiad 2005

September 19, 2005
complex numbers

Problem Statement

Let P1P2P3…P12P_1P_2P_3\dots P_{12} be a regular dodecagon. Show that ∣P1P2∣2+∣P1P4∣2+∣P1P6∣2+∣P1P8∣2+∣P1P10∣2+∣P1P12∣2\left|P_1P_2\right|^2 + \left|P_1P_4\right|^2 + \left|P_1P_6\right|^2 + \left|P_1P_8\right|^2 + \left|P_1P_{10}\right|^2 + \left|P_1P_{12}\right|^2 is equal to ∣P1P3∣2+∣P1P5∣2+∣P1P7∣2+∣P1P9∣2+∣P1P11∣2.\left|P_1P_3\right|^2 + \left|P_1P_5\right|^2 + \left|P_1P_7\right|^2 + \left|P_1P_9\right|^2 + \left|P_1P_{11}\right|^2.
Back to ProblemsView on AoPS