. The principles of projective geometry applied to the straight line and conic . Projective Theorems for the Circle 161 Since the two chords BG^C^ andBA^A^ are drawn through thepoint B to meet the circle inA^,A. and B„B^, BA,.BA, = BC,.BG,.Similarly AG,.AG, = AB,.AB,,GB,.GB,^GA,.GA,. Therefore BA, BA, GB, GB, AA AG, GA, GA,AB,- AB; BG, BG, = 1. Let the points BB^. GG^;BB.,. CG, ■ BB,. GG,; BB,. GG, bedenoted by M, L, L, M, respec-tively, and let 0 be the centre ofthe circle. By Addendum (11)BL. BL _ OB^GL . GL ~ 0C- • If the sides of the triangle aredenoted by a, b, c and the tangentsby «!, Qa
. The principles of projective geometry applied to the straight line and conic . Projective Theorems for the Circle 161 Since the two chords BG^C^ andBA^A^ are drawn through thepoint B to meet the circle inA^,A. and B„B^, BA,.BA, = BC,.BG,.Similarly AG,.AG, = AB,.AB,,GB,.GB,^GA,.GA,. Therefore BA, BA, GB, GB, AA AG, GA, GA,AB,- AB; BG, BG, = 1. Let the points BB^. GG^;BB.,. CG, ■ BB,. GG,; BB,. GG, bedenoted by M, L, L, M, respec-tively, and let 0 be the centre ofthe circle. By Addendum (11)BL. BL _ OB^GL . GL ~ 0C- • If the sides of the triangle aredenoted by a, b, c and the tangentsby «!, Qa, ^1, ^2, Ci, Cn, then fromconsideration of the triangles BLGand BLG sin aCj. sin aco _ BL. BL OB-sin abj,. sin ah, ^^ • ^^ ^^Similarly sin bai. sin ba., _ OG-sin 6ci. sin 6c2 ^^ sin c6i. sin062 _0A- ~ ^^ : ^^ ~ n02•sm ctt]. sm C( ^- Therefore sin ac, sin ac^ sin6ai sin 6c, sin bc2 sincttj sin ba, sin c6, sin cb, sincttg sina6i sinaftg = 1 (i). But from the triangles GGiAand GG,B sin 6cj _AGi sin Asin^^isii^*Substituting this and the simi-lar values in (i) it fo
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Keywords: ., bookcentury1900, bookdecade1910, booksubjectgeometryprojective
