Assignment D (Due Monday Friday 1/16)

This is an assignment to learn but not to turn in. It is a review problem that will be used in class Friday. The problem may be checked in class.

This is review from 444, though you will not recognize it as such until you
write down the lengths.

Be able to prove:

This version has typos that it more interesting: when are two circles similar? Answer: Always. Reason. Two figures are similar if there is a similarity transformation that takes on to the other. See Definition of Similarity Transformation (aka "similitude") in Brown.

Let c be a circle with center O and radius R. Let A and B be 2 points
distinct from O, with the points A' and B' the inversions of A and B in c.
Prove that circle OAB is similar to circle OB'A'.

Intended Version:

Let c be a circle with center O and radius R. Let A and B be 2 points
distinct from O, with the points A' and B' the inversions of A and B in c.
Prove that triangle OAB is similar to triangle OB'A'.
What is the ratio of similitude?

References:

• Sved, p. 37
• Ogilvy, p. 33
• Math 444 Tests and Problems
  • Midterm, Problem 2 (answers on the web)
  • Quiz 3 - Midterm Makeup (comments)
  • Study problems