Wentworth & Hill's Exercise Manuals.(: Geometry

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Ginn, 1884 - Geometry, Plane - 228 pages
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Page 83 - To find the locus of points from which two given circles will be seen under equal angles. Show that the distances from any point in the locus to the centres of the two circles are as the radii of the circles; this reduces the problem to Ex. 12. 17. To find the locus of the points from which a given straight line is seen under a given angle. 18. To find the locus of the vertex of a triangle, having given the. base and the ratio of the other two sides. 19. To find the locus of the points in a plane...
Page xiv - The straight line joining the middle points of two sides of a triangle is parallel to the third side, and equal to half of it.
Page 79 - Find the locus of a point such that the sum of the squares of its distances from two fixed points shall be equivalent to the square of the distance between the fixed points.
Page 62 - In any triangle, the product of two sides is equal to the square of the bisector of the included angle plus the product of the segments of the third side. Hyp. In A abc, the bisector t divides c into the segments, p and q. To prove ab = t
Page 79 - Find the locus of a point such that the difference of the squares of its distances from two given points is equal to a given constant k-.
Page 33 - A cone, whose slant height is equal to the diameter of its base, is inscribed in a given sphere, and a similar cone is circumscribed about the same sphere.
Page 8 - The line which joins the mid-points of two sides of a triangle is parallel to the third side and equal to one half of it.
Page xiv - An isosceles trapezoid is a trapezoid whose non-parallel sides are equal. A pair of angles including only one of the parallel sides is called a pair of base angles. Pairs of base angles The median of a trapezoid is parallel to the bases and equal to onehalf their sum.
Page 62 - In an inscribed quadrilateral, the product of the diagonals is equal to the sum of the products of the opposite sides.
Page xv - In the same circle, or in equal circles, equal arcs are subtended by equal chords ; and, conversely, equal chords subtend equal arcs.

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