Advanced Geometry for High Schools ...

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Copp Clark Company, limited, 1919 - Geometry - 205 pages
 

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Page 18 - If from the vertical angle of a triangle a straight line be drawn perpendicular to the base, the rectangle contained by the sides of the triangle is equal to the rectangle contained by the perpendicular and the diameter of the circle described about the triangle.
Page 19 - Tin; rectangle, contained by the diagonals of a quadrilateral inscribed in a circle, is equal to the sum of the rectangles contained by its opposite sides. Let ABCD be any quadrilateral inscribed in a circle...
Page 18 - If the vertical angle of a triangle be bisected by a straight line which likewise cuts the base, the rectangle contained by the sides of the triangle is equal to the rectangle contained by the segments of the base, together with the square on the straight line which bisects the angle.
Page 33 - To describe an isosceles triangle, having each of the angles at the base double of the third angle.
Page 23 - A point moves so that the difference of the squares of its distances from two fixed points is constant. Show that the locus is a straight line. Hint. Draw XX' through the fixed points, and YY/ through their middle point.
Page 1 - If a straight line cut the sides, or the sides produced, of a triangle, the product of three segments in order is equal to the product of the other three segments.
Page 43 - When four numbers are in musical proportion ; then the first has the same ratio to the fourth, as the difference between the first and second has to the difference between the third and fourth. As in these, 6, 8, 12, 18; where 6 : 18 :: S — 6 : 18 - 12, that is 6 : 18 :: 2 : 6.
Page 68 - 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 54 - B lies on polar of A. Any straight line which passes through a fixed point is cut harmonically by the point, any circle, and the polar of the point with respect to the circle. In a...
Page 68 - In a given indefinite straight line it is required to find a point such that the sum of its distances from two given points on the same side of the straight line shall be the least possible.

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