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Geometry ProblemClick the figure below to see the complete problem 582.Zoom at: Geometry Problem 582
Connect OE,OF,OG,OHWe have E,O,G collinear and F,O,H collinear ( angle bisectors of vertical angles)We also have EG perpendicular to FH at O ( angle bisectors of 2 supplement angles)apply Pythagoras therorem we haveEF^2+HG^2=OE^2+OF^2+OH^2+OG^2=EH^2+FG^2Peter Tran
angle EOF is right angled as the bisectors of a linear pair enclose a right angle. so by applying Pythagoras theorem and associativity property of addition, we have EF^2 +GH^2 = (FO^2 + EO^2) + (HO^2 + GO^2) = (FO^2 + GO^2) + (EO^2 + HO^2) = FG^2 + EH^2.Q. E. D.