. 45. A chord of a circle is divided harmonically byany point on it and the polar of that point. Let {x\ y) be the pole P: then xx + yy = r- is thepolar (P). Also a chord PAB through {x, y) isrepresented by The Cikcle. 99 ^-^ ^ y-y ^ J. I m or x = x + U, y = y + mJi, (1) where k represents the… … Similarly in combining (1) with the equation of thepolar, li must be PQ. Combining (1) with the equation of the circle {x + mf + {^J^mkf = r^or A- + 2(?x + my)k + x^ + y^ - r- = 0,since P + m^ = [.Hence, since PA, PB are the roots of this quadraticin I, PA + PB= - 2{b: + my); PA. PB = x^ + y- - r^…
Geometry, Analytic
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