Selected propositions in geometrical constructions and applications of algebra to geometry. Being a key to the appendix of Davies' Legendre (1875)
Legendre, A. M. (Adrien Marie), 1752-1833, Davies, Charles, 1798-1876 · New York, Chicago [etc.] A.S. Barnes & company · leaf 68
he radii of three equal circles,described within and tangent to, a given circle, and also tangent to eachother. Let O be the centre of thegiven circle, and A, B and C,the centres of the equal in-scribed circles. Denote the radius of thegiven circle by R, and theequal radii of the inscribedcircles… … 62 KEY. Then, in the right-angled triangle ACD, we haveCD2 = AC2 - AD2, or CD2 = 4r2 - r2 = 3r2, or CD = r -y/ST But since O is the point at which lines drawn from the vertices ofthe angles to the middle points of the opposite sides, in both tri-angles, intersect each other, it follows, from Cor.…
Geometry
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