Advanced geometry for high schools : synthetic and analytical (1919)
McDougall, A. H. (Alexander Hiram), 1859-1946 · Toronto : Copp, Clark · leaf 37
P draw PM j_ AB. Let AB = a, AMPA2 - PB2 = k, where a and k are constants.AM24- MP2 = PA2MB2+MP2 = PB2.*. AM2 - MB2 = PA2 - PB2 = h.or x2 - (a - x)2 = k.a2+k and . and x = 2a 24 SYNTHETIC GEOMETRY Hence AM is constant and M is a fixed point. .*. the locus of P is a st. line 1 AB drawn throughthe… … Let P be any point on the radical axis, and drawPM ± AB. Draw the tangents PC, PD to the circles, and joinPA, PB, AC, BD. PA2= PC2+ R2, PB2= PD2 + r2,and, since P is on the radical axis, PC = PD;.-. PA2 - PB2 = R2 - r2, a constant..•., by § 20, the locus of P is a st. line _L AB.Also PA2 =…
Geometry · Geometry, Analytic
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