| George Salmon - 1855 - 376 pages
...- 4y = 7 ; intersecting in [ - — , - — 1 . y 29 29/ Ex. 5. To find in general the equations of **the perpendiculars from the vertices on the opposite sides of a triangle** the co-ordinates of whose vertices are given. Am. (x" - x'")x + (y" - y"")y + (x'x" + y'y'") - (xx"... | |
| Benjamin Hallowell - Geometry - 1872 - 302 pages
...are equal ; hence BE bisects the angle FED. Hence the three perpendiculars let fall upon the three **sides of a triangle bisect the angles of the triangle formed by joining the** points where these perpendiculars intersect the sides.* Remark. — Property 1, above, suggests and... | |
| James McDowell - 1878 - 312 pages
...therefore (172) GD bisects the angle HDE, and BD bisects its supplement. QED NB That the perpendiculars **of a triangle bisect the angles of the triangle formed by joining** their feet is only a particular case of this theorem. It can, however, be easily proved independently.... | |
| Edward Albert Bowser - Geometry - 1890 - 418 pages
...AB is equal to the sum of the products of AC, AE and BD, BE. Apply (335) and (331). 25. AD, BE, CF, **the perpendiculars from the vertices on the opposite sides of a triangle** ABC, intersect in O : prove that the products of AO, OD and BO, OE and CO, OF are equal to each other.... | |
| Levi Leonard Conant - Geometry - 1905 - 140 pages
...same vertex. 455. Construct a triangle, given the feet of the three altitudes. HINT. The altitudes **of a triangle bisect the angles of the triangle formed by joining** their feet in succession. 456. If the inscribed and circumscribed circles of a triangle are concentric,... | |
| Trinity College (Dublin, Ireland) - 1917 - 560 pages
...Show that in a plane triangle ABC, if A = 60°, then V- + cz = o2 + be. 6. What are the lengths of **the perpendiculars from the vertices on the opposite sides of a triangle** whose sides are 19, 20, and 21 yards? 7. Find the lengths of the four common tangents which can be... | |
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