Exercises

On a single Sketchpad sketch, draw each of the following:

1. An equilateral triangle. Be sure that when you drag any of the vertices, the triangle remains equilateral. There are many different ways to do this. We only want to see one of them. Label the vertices and measure the lengths of the sides.

    

2. A triangle with it's inscribed circle. Be sure that when you drag any of the vertices, the circle remains inscribed in the triangle. Label the vertices and measure the radius of the inscribed circle.

    

3. A circle, C, a point, P, outside the circle, and the two segments tangent to the circle passing through the point P. You should also draw, as a dashed curve, the circle through the center of C, P, and the two points of contact, X and Y. This is an easy construction once you understand the mathematics! Remember that the radial segment out to the point of contact of a tangent line is perpendicular to that tangent line. This should give you a hint as to how to draw the dashed circle. Once it is drawn, the points of contact with the tangents are just its intersections with the original circle.

   Your completed sketch should look something like the file attached.