Assignment 3 (Due Wed. 1/28)

3.1 (15 points) This is a problem about the DWEG model with special point O as usual.

1. Draw at random the points O, A, B and construct with straightedge and compass the D-line m that is the D-perpendicular bisector of the D-segment AB. This means that m is the D-line for which the D-reflection of A is B.
2. Write a clear description of the method that you used to make the construction.

3.2 (10 points) Repeat problem 1, except that you will only draw O and A and let B = I, the point at infinity.

3.3 (10 points) Let A and B be points in the Euclidean plane. Consider the elliptic pencil of circles through A and B and the orthogonal hyperbolic pencil.

1. Explain how you can invert this figure to a figure consisting of lines through a point C and circles with center C.
2. Tell why your method works.

You can use Sketchpad for the next two problems if you prefer.

3.4 (10 points) Draw a figure with two parallel lines m and n and a circle c between the lines (but not touching). The center of c should be closer to m than to n.

• Construct the circles that are tangent to m, n and c.

3.5 (15 points) Draw a figure consisting of 3 circles. The circles e and f should be tangent externally and g should be outside both the other circles.

• Use inverstion to convert this figure to a figure like the figure of Problem 4. Invert the circles from problem 4 to construct the circles tangent to e, f, g.