An elementary treatise on modern pure geometry (1893)
Lachlan, Robert · London, New York, Macmillan and Co. · leaf 225
right angle at a limiting point of the system, show that thetangents at P and Q will intersect in a point, the locus of which is a circleof the same system. Let L be the limiting point; and let 0, 0 be the centres of the circles.Let PQ cut the circles again in P and Q. Then if the tangents at P and… … Let LN be drawn perpendicular to PQ; then PI^=PJf.PQ.Therefore PN: PQ = LO : OO; and therefore PF: QN=LO: LO. Similarly QN : P 3^= LO: LO. Hence PP: QQ=LO .LO. Therefore BP :RQ=LO.OP:LO. OQ. Hence the locus of ^ is a circle coaxal with the given circles. Ex. 13. Show that the locus of the point N…
Geometry
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