445 Class Friday 1/14/05

Let P be a point and c be a circle. Let m be a line through P that intersects c in points A and B, then |PA| |PB| is the same number for any line m through P.

Problem 1

Let d = |OP| and let r be the radius of the circle.

• In the special case when line m = line OP, compute |PA| |PB| as an expression in d and r.

• Do this computation for two cases: P outside c and P inside c.

Problem 2

Suppose that line m is a tangent line (so there is only one intersection point T with c). Compute the distance t = |PT| as an expression in d and r. (Hint: Consider the triangle POT.)