### Loci of some orthogonal circles

These two figures give a way to motivate the idea of reflecting a point across a line or across a circle.

#### Case 1. Point C on a segment

(Scroll down for the second case and then some terminology.)

The circle through A and C is orthogonal to segment m. Drag C or double-click the Animate C button to see this "straight" family of circles. What is the other special point on all the circles besides A?

Move A to a new position and repeat the process, observing how the family of circles changes, for example if you drag A onto the segment or to the other side.

#### Case 2. Point K on a circle

The circle through J and K is orthogonal to circle 1. Drag C around circle 1 or double-click the Animate K button to see this "circular" family of circles. How does this compare with the straight family of circles? What is the special point besides J that belongs to this set of circles?

Move J to a new location inside the circle, or on the circle, and repeat the experiment. What does the family of circles look like now?