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Geometry ProblemClick the figure below to see the complete problem 569.Zoom at: Geometry Problem 569
▲ERL, ▲GPJ, ▲LQJ, ▲ENG isoceles ( REL=RLE,90-EAF... )EN + NR = LQ + QR, JQ + PQ = GN + PN, LQ = JQ, GN = EN=> NR + PQ = NP + RQ
Connect G,B, E and note that G, B, E are collinear and EN= GN ( see problem 568)Similarly G,C,J are collinear and PG=PJ . J,D,L are collinear and QJ=QL . E,A,L are collinear and RE=RLWe have NP=PG-NGRQ=RL-QLAnd NP+RQ= PG-NG+RL-QLReplace PG by PJ , NG by NE , RL by RE and QL by QJ we getNP+RQ= PJ-NE+RE-QJ = PQ+NR Peter Tran