. The principles of projective geometry applied to the straight line and conic . 156 Principles of Projective Geometry (7) Show that the square of the distance between a pair of conjugate pointswith respect to a circle is equal to the sum of thepowers of the points. Let the polar of A meet the circle in L and B any point on LAf. Join A to 0 the centreof circle 0 to meet LM in N. Then NM-^. AB^ = Aiy^+BN^ ^AiT^ + iVJiP + BN^-^AJP + + theorem may be stated in a different maimer, viz. : If a quadrangle be inscribed in a circle, the square of the distance between twc
. The principles of projective geometry applied to the straight line and conic . 156 Principles of Projective Geometry (7) Show that the square of the distance between a pair of conjugate pointswith respect to a circle is equal to the sum of thepowers of the points. Let the polar of A meet the circle in L and B any point on LAf. Join A to 0 the centreof circle 0 to meet LM in N. Then NM-^. AB^ = Aiy^+BN^ ^AiT^ + iVJiP + BN^-^AJP + + theorem may be stated in a different maimer, viz. : If a quadrangle be inscribed in a circle, the square of the distance between twcof its diagonal points external to thecircle equals the sum of the squareof the tangents from these points. Describe circles round EBC andFDC meeting in K. K will be onEF for CKE+CKF=ABC+ADC=two right angles. Then EF^ = EK. EF+ FE. FK^ + (8) A and B being two given points in the plane of a given circle, find a pointD on the circle, such that if DA, DB cut the circle again in E, F, the quadrangleABFEia inscribable in a circle.
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Keywords: ., bookcentury1900, bookdecade1910, booksubjectgeometryprojective
