Legendre, A. M. (Adrien Marie), 1752-1833, Brewster, David, Sir, 1781-1868, Davies, Charles, 1798-1876 · New York, Wiley & Long · leaf 96
It may also be demonstrated, that the area ofa triangle is equal to its perimeter multiplied by half the radiusof the inscribed circle. For, the triangles AOB, BOC,AOC, which have a commonvertex at O, have for their com-mon altitude the radius of theinscribed circle ; hence the sumof these… … BOOK IV, 9t PROPOSITION XXXIII. THEOREM. In every quadrilateral inscribed in a circle^ the rectangle of thetwo diagonals is equivalent to the stLtn of the rectangles of theopposite sides. In the quadrilateral ABCD, we shall haveAC.BD - AB.CD + AD.BC. Take the arc CO=AD, and draw BOmeeting the…
Trigonometry · Geometry
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