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" The perpendiculars from the vertices on the opposite sides of a triangle bisect the angles of the triangle formed by joining the feet of the perpendiculars. "
Proceedings of the Edinburgh Mathematical Society - Page 16
by Edinburgh Mathematical Society - 1884
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A Treatise on Conic Sections: Containing an Account of Some of the Most ...

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"...
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Geometrical Analysis: Or the Construction and Solution of Various ...

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...
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Exercises on Euclid and in modern geometry, New ed., revised

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....
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The Elements of Plane and Solid Geometry ...

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....
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Original Exercises in Plane and Solid Geometry

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,...
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The Dublin University Calendar, Volume 1

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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