 | Richard Townsend - Geometry, Modern - 1863 - 328 pages
...sin 1? = e -r- sin (7, therefore pd = bc, qd — ca, rd = ab, and therefore generally — In every triangle the product of any two sides is equal to the product of the diameter of the circumscribing circle into the perpendicular on the third side from the opposite vertex.... | |
 | William Chauvenet - Geometry - 1871 - 380 pages
...AD : AC, whence, ABXAC = AE X AD. PROPOSITION XXI.— THEOREM. 66. In any triangle, the product of two sides is equal to the product of the segments of the third side formed by the bisector of the opposite angle plus the square of the bisector. Let AD bisect the angle A of the triangle ABC; then,... | |
 | William Chauvenet - Geometry - 1872 - 382 pages
...AD : AC, whence, AB X AC = AE X AD. PROPOSITION XXI.—THEOREM. 66. In any triangle, the product of two sides is equal to the product of the segments of the third side formed by the bisector of the opposite angle plus the square of the bisector. Let AD bisect the angle A of the triangle ABC; then,... | |
 | William Chauvenet - Mathematics - 1872 - 382 pages
...AD. PROPOSITION XXI.— THEOREM. 66. In any triangle, the product of two sides is equal to the produd of the segments of the third side formed by the bisector of the opposite angle plus the square of the bisector. Let AD bisect the angle A of the triangle ABC; then,... | |
 | George Albert Wentworth - Geometry - 1877 - 416 pages
...CF to CE, and so also is PH to PB. PROPOSITION XVIII. THEOREM. 299. In any triangle the product of two sides is equal to the product of the segments of the third side formed by the bisector of the opposite angle together -with the square of the bisector. E Let ¿BAС of the ¿\ ABC be bisected by... | |
 | George Albert Wentworth - Geometry - 1877 - 426 pages
...F to СE, and so also is PH to PB. PROPOSITION XVIII. THEOREM. 299. 1n any triangle the product of two sides is equal to the product of the segments of the third side formed bi' the bisector of the opposite anyl e tor/ether with the square of the bisector. ~E Let Z. BA С... | |
 | William Henry Harrison Phillips - Geometry - 1878 - 236 pages
...12, AD = 6, find diameter of the circumscribed circle. XL. Theorem. In any triangle, the product of two sides is equal to the product of the segments of the third side made by a line bisecting the opposite angle, plus the square of that line. HYPOTH. In A ABC, the line... | |
 | Benjamin Gratz Brown - Geometry - 1879 - 68 pages
...the opposite side into segments proportional to the adjacent sides. In any triangle the product of two sides is equal to the product of the segments of the third side formed by the bisector of the opposite angle plus the square of the bisector. Many other properties might be named as belonging to... | |
 | George Albert Wentworth - Geometry, Modern - 1881 - 266 pages
...F to CE, and so also is PH to PB. , PROPOSITION XVIII. THEOREM. 299. In any triangle the product of two sides is equal to the product of the segments of the third side formed by the b'sector of the opposite angle together with the square of the bisector. BÍ ~E Let ZBA С of the Д... | |
 | Franklin Ibach - Geometry - 1882 - 208 pages
...CD :: CE : CB; (237) . (156) QED THEOREM XXIX. 289. In any triangle the product of two sides equals the product of the segments of the third side formed by the bisector of the opposite angle plus the square of the bisector. Let a O be circumscribed about the A ABC, and let the... | |
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In any triangle, the product of two sides is equal to the product of the segments of the third side formed by the bisector of the opposite angle plus the square of the bisector. 
