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 254
The proof is similar when the point 0 is within the circle. Q. E. D. 256. The distances of any two points from the centre ofa given circle are to one another as the distances of each pointfrom the polar of the other. • Let A, B be the two given points, 0 the centre of the givencircle, KG the polar… … Draw AE perpendicular to HO, BF to GO, AC to KH, and BDto KG. Then shall AO : BO :: AC : BD. M. G. 15 226 EXERCISES ON EUCLID [257. Because A and B are the poles of GK and Kff, thereforeOA . OG = OB. OH, since each of these rectangles is equal to thesquare on the radius, and because the angles AFB…
Geometry
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