The figure below shows a semicircle of
center O, diameter AB, radius R and equal arcs AC, CD, DE, EF, FG, GH,
HI, IJ, JB. Chords CJ, DI, and EH intersect OF and OG at K, L, M, N, P,
Q, respectively. Prove that FG + PQ + MN + KL = R.
Try to use elementary geometry (Euclid's Elements.)