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 34
Prop. XXXVIII.—Find a point, in the prolongation of any diam-eter of a given circle, such that a tangent from it to the circumferenceshall be equal to the diameter of the circle. Solution.—Let C be the centre of the given circle, and let AB beany diameter. At B, draw BP perpendicular to ABand equal… … 28 KEY. The triangles CQT and CBP have the common angle PCT; theangles CQT and CBP are equal, because they are right angles; andthe sides CQ and CB are equal, because they are radii of the samecircle: hence, these triangles are equal in all their parts, and conse-quently, QT = BP = AB; T is…
Geometry
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