An elementary treatise on modern pure geometry (1893)
Lachlan, Robert · London, New York, Macmillan and Co. · leaf 86
BCD, and if any fifth point E be taken on the circle, show thatthe projections of 0 on the Simson lines of the tetrastigms BCDE, CDEA,DEAB, EABC, ABCD also he on a straight line. Show that the theorem may be extended. [E. M. Langley, E. T. Reprint, Vol. li., p. 77.] 122. Ex. 1. If the lines… … It is easy to prove that the angles BAC, YXZ are each equal to thedifiference of the angles BOC, BAC. Hence the theorem follows at once. Since the triangles BOC, COB are similiir, we haveEC: OB=BC: CO. 70 THE NINE-POINT CIRCLE ™ . AO.BC AO.CO.BO Therefore __=____. Hence, if ^S be the centre of the…
Geometry
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