| 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... | |
| 394 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 - 608 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... | |
| Debashis Dutta - 2006 - 954 pages
...in two distinct points then the line is called (a) Tangent line (b) Normal (c) Secant (d) None 11. **A point moves so that the sum of the squares of its distances from** the six faces of a cube is constant. The locus of this point is a (a) Circle (b) Sphere (c) Ellipse... | |
| B.K. Dev Sarma - 2003 - 676 pages
...y respectively. Show that the locus of its centre of the circle is дс* - уг = аг - Ьг. 25. **A point moves so that the sum of the squares of its distances from** the three points (x\, >¡), (ль, уг) and (дез, >з) is constant (= <f). Prove that the locus... | |
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