 ... it has one pair of opposite angles equal. 3. If in a quadrilateral ABCD, AB be equal to AD and BC to DC, the diagonal AC bisects each of the angles BAD, BCD. 4. If in a quadrilateral ABCD, AB be equal to AD and BC to DC, the diagonal BD is bisected...  Mathematical Questions and Solutions - Page 261869Full view - About this book
 | 1868 - 380 pages
...= JL(-X + Y + Z):( ) : ( ), sin A in terms of are:\l coordinates of centre, _ , sin A sin B sill U the coordinates being referred to the triangle whose...in the question. 2. Again, for the inscribed conic (Ix) + (">y) + (nz) = ", 0 = Zlmn (I sin B sin C + m sin A sin C + n sin A sin B), 6*= P + ms + n2... | |
 | W. J. C. Miller - Mathematics - 1869 - 120 pages
...2(/cosA+£ cosB + A cosC). But f:g:* = JL( sin A in terms of areal coordinates of centre, BUI A sm B sin C the coordinates being referred to the triangle...in the question. 2. Again, for the inscribed conic (Ix) + (my) + (nz) = 0, 0 = 2lmn (I sin B sin C + m sin A sin C + n sin A sin B), 0'= Z2 + m" + n2+2mn... | |
 | George Albert Wentworth - 1889 - 276 pages
...product of one of its legs, and the distance of this leg from the middle point of the opposite side. 9. The triangle whose vertices are the middle points of the sides of a given triangle is equivalent to one-fourth of the given triangle. 10. The figure whose vertices are... | |
 | George Albert Wentworth - 1889 - 264 pages
...product of one of its legs, and the distance of this leg from the middle point of the opposite side. 9. The triangle whose vertices are the middle points of the sides of a given triangle is equivalent to one-fourth of the given triangle. 10. The figure whose vertices are... | |
 | George Irving Hopkins - 1891 - 210 pages
...the product of one of its legs and the distance of this leg from the middle point of the other. 441. The triangle whose vertices are the middle points of the sides of a given triangle is equivalent to one-fourth the latter. 442. The parallelogram formed in 101 is equivalent... | |
 | Henry Martyn Taylor - 1893 - 486 pages
...equal to AD and BC to DC, the diagonal BD is bisected at right angles by the diagonal AC. 5. Prove that the triangle, whose vertices are the middle points of the sides of an equilateral triangle, is equilateral. 6. Prove that the triangle, formed by joining the middle points... | |
 | Henry Martyn Taylor - Euclid's Elements - 1895 - 708 pages
...equal to AD and BC to DC, the diagonal BD is bisected at right angles by the diagonal AC. 5. Prove that the triangle, whose vertices are the middle points of the sides of an equilateral triangle, is equilateral. 6. Prove that the triangle, formed by joining the middle points... | |
 | Julian Lowell Coolidge - Circle - 1916 - 614 pages
...113.] The centre of Taylor's circle lies on the Simson line of the foot of each altitude ivith regard to the triangle whose vertices are the middle points of the sides of the given triangle. The perpendicular from Mf on HajHa^ bisects (HatHak) since (MiHa:) = (M^Ha^). The perpendiculars... | |
 | Julian Lowell Coolidge - Circle - 1916 - 603 pages
...circle, and exhibit its analogies to the nine-point circle as follows : Nine-point circle. Circumscribed to the triangle whose vertices are the middle points of the sides. Radius one-half that of circumscribed circle. Centre of gravity and orthocentre are internal and external... | |
 | 268 pages
...and LBEA= LDEA; but BED is a st. line; .'. L s BE A, DEA are rt. L s. (Def. 11.) 25, 5. Prove that the triangle, whose vertices are the middle points of the sides of an equilateral triangle, is equilateral. Let ABC be given A , and D, E, F mid. pts. of BC, CA, AB resply.... | |
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