ON^2 = OD^2 + DN^2 - 2*OD*DN*cos 27
R^2 = R^2 + DN^2 - 2*R*DN*cos 27
DN^2 = 2*R*DN*cos 27
DN = 2*R*cos 27
Теперь также по теореме косинусов
DN^2 = ON^2 + OD^2 - 2*OD*ON*cos DON
4R^2*cos^2 27 = 2R^2 - 2R^2*cos DON
2cos^2 27 = 1 - cos DON
cos DON = 1 - 2cos^2 27 ~ -0,588
DON = 126
MOD = 180 - 126 = 54