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altitude Analysis angle base bisector centre chord circumference circumscribed construct containing cubic cylinder denote described determine diagonals diameter difference distance divide draw drawn edge equal equidistant equilateral triangle equivalent feet figure Find the area Find the volume formed four frustum given circle given line given point given triangle greater half height hexagon hypotenuse inches inscribed intersection isosceles triangle join lateral legs length line parallel mean measures meet middle points opposite parallel parallelogram passes perimeter perpendicular plane problem produced proportional Prove pyramid quadrilateral radii radius ratio rectangle regular regular polygon respectively rhombus right cone right triangle secant segment sides similar slant height solution sphere square square feet straight line tangent Theorem third touch trapezoid triangle ABC vertex vertices volume wide yards
Page 31 - Find the radii r, r' of the inscribed and circumscribed spheres, the surface S, and the volume V. 9. The same exercise for the regular octahedron. 11. The same exercise for the regular tetrahedron. 12. The same exercise for the regular octahedron. 13. The height of a frustum of a right cone is h, and the radii of its bases r, r' ; what is the volume of the largest regular four-sided frustum which can be made from it? 14. The volume of a right cone, whose slant height is equal to the diameter of its...
Page 8 - A pyramid 15 ft. high has a base containing 169 sq. ft. At what distance from the vertex must a plane be passed parallel to the base so that the section may contain 100 sq.
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 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 7 - The sum of the diagonals of a quadrilateral is less than the sum and greater than half the sum of tht. sides. * 21. Each side of a triangle is less than half the perimeter.
Page 62 - In every inscribed quadrilateral the product of the diagonals is equal to the sum of the products of the opposite sides.
Page xxvi - Theorem. The perimeters of two regular polygons of the same number of sides have the same ratio as their radii, or as their apothems.
Page 67 - Every straight line cutting the sides of a triangle (produced when necessary) determines upon the sides six segments, such that the product of three non-consecutive segments is equal to the product of the other three.
Page 83 - OP= 4 inches, r = 4 inches. 16. 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...