This is an assignment to learn but not to turn in. It contains the basics of what you should have in your toolkit to understand well the class on Wednesday. Be prepared to state the "facts" or answer the questions indicated below during class Wednesday.
Review the statements and proofs of the theorems about lengths PA and PB when A and B are on a circle c and P, A, B are on a line that is a secant or a chord of a circle. Also include the special case when the line is a tangent (so A = B). Be prepared to state the theorems, apply the theorems, or outline a proof of the theorems.
References:
Definition: State clearly what it means for two circles c and d with centers C and D to be orthogonal.
Theorem Statement: Suppose c and d are orthogonal circles with centers C and D. If T is the point of intersection of c and d, be able to state a relationship among the 3 lengths |CT|, |DT| and |CD|.
References:
Orthogonal circle and line: If c is a circle with center C and m is a line. What must be true about the line m for m and c to be orthogonal?
Constructing an orthogonal circle given the center: Given a circle c with center C and a point D outside the circle, how can one construct a circle d with center D so that d is orthogonal to c?