...are « cos A— /?cos£=0, /Jcos-B— 7- cos (7=0, ? cos C— a cos A=0. 278. Theorem. — The three perpendiculars erected at the middle points of the sides of a triangle meet in one point. For (Ex. 4, p. 221) we have found their equations to be n sin A — /? sin B + y...

...is equally distant from the three sides of the triangle. PROPOSITION XLI.— THEOREM. 130. The three perpendiculars erected at the middle points of the sides of a triangle meet in the same point. Let DG, EH, FK, be the perpendiculars erected to BC, CA, AB, respectively,...

...is equally distant from the three sides of the triangle. PROPOSITION XLI.—THEOREM. 130. The three perpendiculars erected at the middle points of the sides of a triangle meet in the same point. Let DG, EH, FK, be the perpendiculars erected to BC, CA, AB, respectively,...

...The area of a circle beiug denoted by c-, find its radius and circumference. 2. Prove that the three perpendiculars erected at the middle points of the sides of a triangle meet in a point. Prove that tho chord of au arc of GO1 is equal to the radius. 3. Prove that the area...

...shall be equal. 16. \Vhat axiom is implied in the last line of the proof of the theorem in § 87? 17. The perpendiculars erected at the middle points of the sides of a triangle meet in one point. Hints. — Erect two of the perpendiculars; show (by II. Law of Equality) that their...

...mutually perpendicular. Ans. b = o, b2 — a2 = i. (n.) Choosing the axes as in § 27, Ex. 9, prove that the perpendiculars erected at the middle points of the sides of a triangle meet in the point ( -2, — V 2 (12.) In a similar manner, show that the perpendiculars from the vertices...

...lies in CD; (102) .•. the bisectors AE, BF, and CD meet in a common point. QED THEOREM XXXVII. 105. The perpendiculars erected at the middle points of the sides of a triangle meet in a common point. In the A ABC, let DH, FG, and EM be respectively _L to AC, AB,a,nd BC, at their...

...theorem. 29. The bisectors of the angles of a triangle meet in a point equidistant from the sides. 30. The perpendiculars erected at the middle points of the sides of a triangle meet in a point equidistant from the three vertices. 31. Lines drawn through the vertices of a triangle,...

...and OA'&a a radius will pass through the vertices of the triangle. For the point of intersection of the perpendiculars erected at the middle points of the sides of a triangle is equally distant from the vertices of the triangle (§ 128). 233. SCHOLIUM. The above construction...

...through one point ? 21. Prove that the three altitudes of a triangle meet in one point. 22. Prove that the perpendiculars erected at the middle points of the sides of a triangle meet in one point. 23. Prove that the three medians of a triangle meet in one point. Show also that...