Exercises on Euclid and in modern geometry for the use of schools, private students, and junior university students (1881)
McDowell, James L · Cambridge, Deighton, Bell, and Co. · leaf 269
ir polars (244), therefore the angle AOB isa right angle, that is, OB is perpendicular to OA, and it meetsthe side opposite to A in D. In like manner it can be provedthat the angles BOE and COF are right angles; also B, F, Eare in the same straight line, viz. the polar of /. Hence thereciprocal… … Let 0 be the centre of the given circle, AB & tangent to it atany point P; join OP meeting the auxiliary circle in E, and makeOP. OP = 0R\ then P is the pole of P. Therefore OP is constant. Hence the required locus is theconcentric circle with radius OP. Q. E. D. 1ST. B. If we draw the tangent…
Geometry
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