Legendre, A. M. (Adrien Marie), 1752-1833, Brewster, David, Sir, 1781-1868, Davies, Charles, 1798-1876 · New York, Wiley & Long · leaf 64
PROBLEM XV. To inscribe a circle in a. given tîiangle. Let ABC be the given triangle. Bisect the angles A and B, bythe lines AO and BO, meeting inthe point O ; from the point O,let fall the perpendiculars OD,OE, OF, on the three sides of thetriangle: these perpendiculars willall be equal. For, by… … BOOK III. 69 lion, we have the angle DAO = OAF, the right angle ADO =AFO ; hence the third angle AOD is equal to the tiiird AOF(Book I. Prop. XXV. Cor. 2.). INIoreover, the side AO is com-mon to the two triangles AOD, AOF ; and the angles adjacentto the equal side are ecjual : hence the triangles…
Trigonometry · Geometry
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