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" The perpendicular bisectors of the sides of a triangle meet in a point. 12. The bisectors of the angles of a triangle meet in a point. 13. The tangents to a circle from an external point are equal. 14... "
Plane and Solid Geometry - Page 65
by Isaac Newton Failor - 1906 - 418 pages
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Report of the Board of Education

Bombay (India : State). Board of Education - Education - 1851 - 768 pages
...hisector of the angle between the two lines, what is the form of the equation ? 1 1 . Hence prove that the bisectors of the angles of a triangle meet in a point. 12. Find the equation of a straight line, in terms of the perpendiculars on it, from the origin and...
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First Mnemonical Lessons in Geometry, Algebra, and Trigonometry

Thomas Penington Kirkman - Mathematics - 1852 - 236 pages
...see that it is the bisector of the angle CBA ; for [22] DBe and DBg have equal sines. Thus the three bisectors of the angles of a triangle meet in a point, which is the centre of the inscribed circle. By Prop. B. (20), AC x Df+ BC*De + ABxDg= twice the area of the...
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The Mathematical Monthly, Volume 2

John Daniel Runkle - Mathematics - 1860 - 460 pages
...bisectors of the angles of this triangle, and since their sum vanishes identically, we have the proof that the bisectors of the angles of a triangle meet in a point. Again, if S = 0 and 6" = 0 are the equations of two conies, then S -|- k S' = 0 is that of the conic...
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The Mathematical Monthly, Volume 2

1860 - 462 pages
...bisectors of the angles of this triangle, and since their sum vanishes identically, we have the proof that the bisectors of the angles of a triangle meet in a point. Again, if S = 0 and S" = 0 are the equations of two conies, then S _|_ t g' = о is that of the conic...
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Report of the Board of Education

Bombay (India : State). Board of Education - Education - 1851 - 764 pages
...bisector of the angle between the two lines, what is the form of the equation ? 11. Hence prove that the bisectors of the angles of a triangle meet in a point. 12. Find the equation of a straight line, in terms of the perpendiculars on it, from the origin and...
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A school Euclid, being books i. & ii. of Euclid's Elements, with notes by C ...

Euclides - 1874 - 120 pages
...Conditions of Equality. Props. 4, 8, 26, 5 and 6. 1. The perpendiculars from the middle points of two sides of a triangle meet in a point which is equidistant from the three angles of the triangle. 2. Find a point within an acute-angled triangle from which a circle may...
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Modern geometry [ed.] with an appendix by W.B. Jack

Richard Wormell - 1876 - 268 pages
...given side. 58. A ladder is gradually raised against a wall : find the path of its middle point. 59. The bisectors of the angles of a triangle meet in a point. 60. The perpendiculars to the sides of a triangle at their middle points meet in a point. 61. The perpendiculars...
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The solution of geometrical exercises, explained and illustrated; with a ...

Charles Mansford - 1879 - 112 pages
...Conditions of Equality. Props. 4, 8, 26, 5 arid 6. 1. The perpendiculars from the middle points of two sides of a triangle meet in a point which is equidistant from the three angles of the triangle. 2. Find a point within an acute-angled triangle from which a circle may...
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Geometrical Exercises for Beginners

Samuel Constable - Geometry - 1882 - 222 pages
...the angles OBD, OCD, respectively. The triangle BAC, thus formed, is the required one. Join OA. Since the bisectors of the angles of a triangle meet in a point (22), and the angles B, C, are bisected by construction, 0 is the centre of the inscribed circle. Hence...
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Exercises on the geometry and measurement of plane figures, being solutions ...

Richard Wormell - Geometry, Plane - 1883 - 210 pages
...And, since OD is constant, ... О B is constant : Therefore the path is the quadrant of a circle. 59. The bisectors of the angles of a triangle meet .in a point. For the intersection of any two of them determines a point which is equally distant from the -three...
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