This is considered part of the assessment of what you know about orthogonal circles. Another part will be the test on Friday, March 3.
You can consult other students, but the writing should be entirely your own. So talk but then go away and write independently.
Answer these questions. The answers are little paragraphs or proofs or essays. Write clearly, correctly, and completely (and neatly).
Define the concept of inversion of a point in a circle and also tell what it means for two circles to be orthogonal. Then explain clearly how inversion of a point is related to orthogonal circles. This may include an if and an only if. How can this be extended to a case where a "circle" is a Euclidean line?
Define the radical axis of two circles. Prove that the radical axis is a line, and also prove that for three circles the three radical axes of the three pairs of circles are concurrent or parallel. Tell how these results can be used to construct a circle orthogonal to 3 given circles (when the construction is possible).
In the DWEG model, explain in terms of Euclidean objects what are parallel D-lines and perpendicular (orthogonal) D-lines. Then if the D-perpendicular bisector of D-points A and B is the D-line m so that D-reflection in m takes A to B, what E-object is m and how is it constructed?