(a) Print a DWEG parallelogram and mark the equal angles.
(b) Print a DWEG circle with DWEG center A through DWEG point B.
(c) Construct and print two "random" DWEG squares. Jot a brief explanation of the construction.
(d) Construct and print two "random" DWEG equilateral triangles. Jot a brief explanation of the construction.
(a) State the definition of an Apollonian circle of A and B (as a locus).
(b) Prove from the definitions that an Apollonian circle of A and B inverts A to B.
(c) Draw 3 points A and B and P. construct the Apollonian circle of A and B through a point P. The construction should work for a random P.
(d) Draw two points A and B. Construct the Apollonian circles of A and B with ratios 1/3, 1/2, 2, 3, and also 1.
(a) (DWEG circles are Apollonian) In Lab 4, recall that a DWEG circle with center A through B was obtained by inverting B through the circles representing DWEG lines to get points B' and B''. Then the DWEG circle was constructed as the circle through B, B' and B''. Prove that this circle is actually the Apollonian circle of A and O through B.
(b) (Points symmetric by two mirrors) Given two disjoint circles c and d, prove that there is exactly one pair of points A and B such that the inversion of A is B, both with mirror c and with mirror d. Hint: If the circles are concentric, this is much easier.
(c) Draw two disjoint circles c and d, one inside the other. Construct the points A and B of part (b). Then construct a circle m so that inversion of c and d in m are concentric circles.
(a) Draw a circle and inscribe a square in the circle. Construct the image of inversion of the square in the circle.
(b) Construct a circle with a triangle circumscribed around it. Then construct the inversion image of the triangle.
(c) Construct two circles c and d that intersect at points C and D and a circle e orthogonal to both c and d. Then draw the circle mwith center C that passes through D. Conctruct the images of the circles c, d and e by inversion in m.