Mathematical Experiment 2

  1. Draw three nonoverlapping circles of three different sizes anywhere on the plane. For each pair of circles draw their two common tangents. Show that the intersection of three pairs of tangents lie on a straight line. This is known as Monge's Theorem. The resulting configuration should be readjustable depending on the location and the size of each circle.
  2. Use Maple to find the equations of the eight circles tangent to the three circles with equations given by
  3. (x-3)2+y2 = 0.4
    x2+y2 = 1
    (x-2)2+(y-2)2 = 1.5

    Draw the resulting circles by means of any software.

  4. Given a point P on the circumcircle of a triangle, the feet of the perpendiculars from P to the three sides all lie on a straight lin. This line is commonly called the Simson line of P with respect to the triangle. Dsiplay the configurations when P moves around the circumcircle.
  5. Rotate a cube along one of its edges step by step, as seen from infinite.