Advanced geometry for high schools : synthetic and analytical (1919)
McDougall, A. H. (Alexander Hiram), 1859-1946 · Toronto : Copp, Clark · leaf 38
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 =… … Let A, B be the centres of the circles. Describe a circle with centre O cutting the givencircles at C, D and E, F. Draw CD, EF and producethem to meet at P. Draw PM j_ AB. Draw tangentsPG, PH to the circles. Show that PM is the required radical axis. SYNTHETIC GEOMETRYSecond Method
Geometry · Geometry, Analytic
Internet Archive · Western University Libraries · Public Domain Mark 1.0. Free to use for anything.
