An elementary treatise on modern pure geometry (1893)
Lachlan, Robert · London, New York, Macmillan and Co. · leaf 182
the circle in the pointsP, P and Q, Q respectively: show that if the pencil A {PQ, BC) be harmonic,then B and C will be the other centres of the tetrastigm PPQQ^. Ex. 6. Show how to inscribe a triangle in a given circle, so that its sidesshall pass respectively through three given points. Let A, B,… … DE cut the circle in the points X, X; Y, F; Z, Z; respectively. Thenthese points determine two triangles XYZ, XYZ which satisfy the givenconditions. For, since AD, BE, OF are concurrent (§ 267), it follows (§ 96, Ex. 11)that D {GA, EF} is harmonic. Therefore A is one of the centres of thetetrastigm…
Geometry
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