Let A = (3, 4), B = (0, −5), and C = (4, −3). a) Find equations for the perpendicular bisectors of segments AB and BC, and coordinates for their common point K.

b) Calculate lengths KA, KB, and KC.

c) Why is K also on the perpendicular bisector of segment CA?

d) A circle centered at K can be drawn so that it goes through all three vertices of triangle ABC. Explain. This is why K is called the circumcenter of the triangle. In general, how do you locate the circumcenter of a triangle?