An elementary treatise on modern pure geometry (1893)
Lachlan, Robert · London, New York, Macmillan and Co. · leaf 225
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… … PROPERTY OF A CYCLIC TETRASTIGM. 209 points of the former cut the latter in the points P, Q; P, Q; respectively.If i be a limiting point of the system, show that PP : QQ=PL+PZ : QL + QL.By § 332, (ii), we have, if R, R be the points of contact of PQ, PQ, PR : PL = PR : PL=QR : QL^QR : QL.Let PQ cut…
Geometry
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