13th Australian 1992 Problem A1 P, Q, R are adjacent vertices of a regular 9-gon with center O. M is the midpoint of the segment joining O to the midpoint of QR and N is the midpoint of PQ. Find the ∠ONM.
Let L be the midpoint of QR. ∠POQ = 360 o /9 = 40 o , so ∠POL = 60 o . But OP = OL, so POL is equilateral. Hence PM is perpendicular to OL. Obviously ON is perpendicular to PQ, so M and N lie on the circle diameter OP. Hence ∠ONM = ∠OPM = 30 o . 13th Aus 1992 © John Scholes jscholes@kalva.demon.co.uk 5 February 2004 Last updated/corrected 5 Feb 04