Original Exercises in Plane and Solid Geometry |
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ABCD adjacent sides altitude angle bisector angle formed area is equal auxiliary triangle base angles bisected circle whose center circles intersect circumscribed circle collinear common chord common tangent concyclic Construct a circle Construct a triangle diagonals diameter difference distance draw a line equal circles equal in area equilateral triangle Find a point find the area find the locus given angle given circle orthogonally given length given line given point given square given triangle Hint hypotenuse inscribed circle inscribed quadrilateral isosceles triangle joining the middle legs line drawn line joining line of centers line parallel middle points opposite angle opposite sides orthocenter parallelogram perimeter perpendicular plane points of intersection polygon problem problem of Apollonius radical axis radii radius ratio rectangle required circle respectively rhombus right angle right triangle secant segments similar triangles sphere straight line tangent externally tangents drawn theorem third side trapezoid triangle ABC vertex
Popular passages
Page 10 - 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 69 - In any triangle the product of two sides is equal to the altitude upon the third side, multiplied by the diameter of the circumscribed circle.
Page 71 - In every triangle the sum of the squares of two sides is equal to twice the square of half the third side plus twice the square of the median drawn to the third side.
Page 68 - In any triangle, the product of two sides is equal to the product of the segments of the third side formed by the bisector of the opposite angle plus the square of the bisector.
Page 18 - If two triangles have two sides of the one equal respectively to two sides of the other, but the included angle of the first greater than the included angle of the second, then the third side of the first is greater than the third side of the second. Given A ABC and A'B'C...
Page 123 - Solution 1. First determine the ratio of the linear speeds of the weight and the point at which the force F is applied. If the worm is assumed to make one turn in a unit of time the handle will have a speed equal to the circumference of a circle whose radius is the distance from the axis of the worm to the center of the handle. Therefore, it would be 2irl6 in.
Page 77 - 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 28 - Prove that the locus of the vertex of a triangle, having a given base and a given angle at the vertex, is the arc which forms with the base a segment capable of containing the given angle (§ 318).