 | G. P. West - Geometry - 1965 - 362 pages
...described; through X a line is drawn cutting the circle at R, S. Show that XR2 + RY2 = XS2 + S Y2. 12. A point moves so that the sum of the squares of its...is a circle having for centre the mid-point of AB. 13. Prove that the sum of the squares on the sides of a parallelogram is equal to the sum of the squares... | |
 | James McMahon - 2018 - 244 pages
...; then eliminate OB2.) tEx. 1140. In the figure of Ex. 1139, OA' + OD2=OB2 + OC2 + 4BC2. |Ex. 1141. A point moves so that the sum of the squares of its...is a circle, having for centre the mid-point of AB. tEx. 1142. The sum of the squares on the sides of a parallelogram is equal to the sum of the squares... | |
 | Ray C. Jurgensen, Alfred J. Donnelly, Mary P. Dolciani - Geometry - 1963 - 198 pages
...generalized theorem, of which Apollonius' theorem is a particular case. Also compare Ex. 27.) Ex. 3O. A point moves so that the sum of the squares of its...remains constant ; prove that its locus is a circle. Ex. 31. The sum of the squares on the sides of a parallelogram is equal to the sum of the squares on... | |
 | Thomas Tate (Mathematical Master, Training College, Battersea.) - 1860 - 404 pages
...(i) on to the base, (ii) on to the base produced ? tEx. 2 14. A point moves so that the sum of tbe squares of its distances from two fixed points A,...is a circle having for centre the mid.point of AB. I CIRCLE. ARCS AND CHORDS. tEx. 215. PQ, PR are a chord and a diameter meeting at a point P on the... | |
 | 480 pages
...Apollonius' theorem become if the vertex moves down (i) on to the base, (ii) on to the base produced? Ex. 64. A point moves so that the sum of the squares of its...fixed points A, B remains constant; prove that its loons is a circle having for centre the mid-point of AB. Ex. 66. The base AD of a triangle OAD is trisected... | |
 | University of St. Andrews - 1905 - 682 pages
...Find an expression for the distance between two points in terms of their co-ordinates. The point P moves so that the sum of the squares of its distances from two fixed points A and B, is constant ; prove that its locus is a circle whose centre is midway between A and B. 9. Find... | |
 | H.K. Dass & Rama Verma - Mathematics - 1032 pages
...Show that the points (0, 4, 1), (2, 3, -1), (4, 5, 0), (2, 6, 2) are the vertices of a square. 15. A point moves so that the sum of the squares of its distances from the six faces of a cube is constant. Show that its locus is a sphere. 16. Find the locus of the point... | |
 | 392 pages
...distances from the equal sides. Find its locus. [Take base y = 0 and sides of gradient ±ni.] Ex. 30. A point moves so that the sum of the squares of its distances from the sides of a triangle is fixed. Find its locus. [Take base ;/..=<) and sides of gradients i«, and... | |
 | 352 pages
...lines meet, and the area of the triangle whose corners are (0, 0), (0, 8) and this meeting-point. 6. A point moves so that the sum of the squares of its distances from the three points (0, 4), (0, - 4), (6, 3) is 362. Find the equation of its locus. Show that this locus... | |
 | University of St. Andrews - 1898 - 610 pages
...circles — and find the angle between those diameters of these which pass through the origin. 14. A point moves so that the sum of the squares of its distances from the sides of an equilateral triangle is constant, = fc2, say. Show that the locus of the point is a... | |
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A point moves so that the sum of the squares of its distances from the points (0, 0), (1, 0) is constant. 
