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ABCD AC and BD altitude apothem arc BC base bisectors bisects chord circle whose center circumference circumscribed coincide cone consequently const cylinder Data Denote diagonals AC diameter dihedral dihedral angles distance Draw AC edge EFGH equiangular equiangular polygon equidistant equilateral triangle equivalent exterior angle frustum given line given point given radius given side hence hexagon hypotenuse intersecting isosceles trapezoid isosceles triangle line drawn meeting middle point parallel lines parallelogram parallelopiped pass a plane perimeter perpendicular plane MN polygon produced Proof prove pyramid Q-ABC quadrilateral radii ratio rectangle regular inscribed respectively rhombus right angle right triangle secant segment Similarly Solution sphere spherical square surface tangent tetrahedron trapezoid trihedral vertex vertical angle whence
Page 270 - If in a right triangle a perpendicular is drawn from the vertex of the right angle to the hypotenuse : I.
Page 71 - DE and on the same side of it ; but equal triangles on the same base, and on the same side of it, are between the same parallels ; [I.
Page 288 - ... that the angles which this straight line makes with the first three are together less than the sum, but greater than half the sum, of the angles which the first three make with each other.
Page 65 - O two perpendiculars OM and ON are drawn to the chords AB and CD respectively, and it is known that Z NMO = Z ONM. Prove that AB = CD. 5. Two circles intersect at the points A and B. Through A a variable secant is drawn, cutting the circles at C and D. Prove that the angle DBC is constant. 6. Let A and B be...
Page 208 - The section of a pyramid made by a plane parallel to the base is similar to the base.
Page 246 - If one of the equal sides of an isosceles triangle is produced through the vertex by its own length, the line joining the end of the side produced to the nearer end of the base is perpendicular to the base.
Page 146 - Three times the sum of the squares on the sides of a triangle is equal to four times the sum of the squares on the medians.
Page 121 - The perpendicular from any point of a circumference upon a chord is a mean proportional between the perpendiculars from the same point upon the tangents drawn at the extremities of the chord.