 The perpendiculars from the vertices of a triangle to the opposite sides meet in a point. Let the Js be AH, BP, and CK. Through A, B, C suppose B'C', A'C', A'B', drawn II to BC, AC, AB, respectively. Then AH is _L to B'C'. (Why ?) Now ABCB' and A CBC'...  Vector Analysis: A Text-book for the Use of Students of Mathematics ... - الصفحة 106بواسطة Edwin Bidwell Wilson, Josiah Willard Gibbs - 1901 - عدد الصفحات: 436عرض كامل - لمحة عن هذا الكتاب
 | Alexander H. McDougall - 1919 - عدد الصفحات: 232
...,. BG BD эг, by alternation, ^c = DC' Л. G coincides with D. Л AD, BE, С F are concurrent. 5. The perpendiculars from the vertices of a triangle to the opposite sides are concurrent. Fut. 9. In Д ABC, draw AX _L BC, BY _|_ ÇA, CZ J_ AB. To prove that AX, BY, CZ are... | |
 | 1927 - عدد الصفحات: 324
...perpendicular bisectors of the sides of a triangle. 34. The bisectors of the angles of a triangle. 35. The perpendiculars from the vertices of a triangle to the opposite sides. 36. The medians of a triangle. 37. A copy of a given geometric design. C. MAKING CORRECT INFERENCES... | |
 | David Eugene Smith, William David Reeve - 1927 - عدد الصفحات: 426
...perpendicular bisectors of the sides of a triangle. 34. The bisectors of the angles of a triangle. 35. The perpendiculars from the vertices of a triangle to the opposite sides. 36. The medians of a triangle. 37. A copy of a given geometric design. K. Making Correct Inferences... | |
 | William Duncan MacMillan - 1927 - عدد الصفحات: 460
...C, is B' + C'- A\ A' + C'- B2 ' ' '~ 2C> ' 2C2 • 14. Prove that the perpendiculars from the three vertices of a triangle to the opposite sides meet in a point. 15. If, in problem 13, the vector P terminates at the intersection of the three perpendiculars (the... | |
 | William Leonard Schaaf - 1928 - عدد الصفحات: 176
...perpendicular bisectors of the sides of a triangle. q. The bisectors of the angles of a triangle. r. The perpendiculars from the vertices of a triangle to the opposite sides. s. The medians of a triangle. t. A copy of a given geometric design. E. Psychological Considerations... | |
 | Military Academy, West Point - عدد الصفحات: 906
...Theorem: The bisectors of the citerior angles of a rhombus inclose a rectangle. No. 2.— Theorem: The perpendiculars from the vertices of a triangle to the opposite sides meet in a point. (Wt. 10.) No. 3. —Problem: To find the locus of the intersection of the diagonals of the parallelogram... | |
 | عدد الصفحات: 440
...and AC, BD. Hence also AB, CD is also a rectangular hyperbola, ie AB is at right angles to CD. Thus: The perpendiculars from the vertices of a triangle to the opposite sides meet in a point (the orthocentre). Also Every conic through the vertices of a triangle and the orthocentre is a rectangular... | |
 | Actuarial Society of America - 1921 - عدد الصفحات: 656
...vote and in how many ways will the votes be equally divided among the candidates ? 11 (a) Show that the perpendiculars from the vertices of a triangle to the opposite sides meet in a point. (5) If from a point within an equilateral triangle, perpendiculars are drawn to the three sides, show... | |
 | Actuarial Society of America - 1927 - عدد الصفحات: 480
...intersect in F. Prove that the triangle BFC is equal in area to the quadrilateral ADFE. 11. Prove that the perpendiculars from the vertices of a triangle to the opposite sides meet in a point. 12. (a) Write down and simplify an expression for the numerical value of : cos [cor1 (-T) - cos"1 ~5~]... | |
 | B.K. Dev Sarma - 2003 - عدد الصفحات: 676
...5+42 2(-4 + 48)-(6 + 60)-(12+10) 88-66-22 0 Therefore, the three lines are concurrent Example 14 Prove the perpendiculars from the vertices of a triangle to the opposite sides meet at a point. Ans: Without loss of generality, let us take the vertices of the triangle ABC as A(0, 0),fi(a,0)andC(x',yO.... | |
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