Using Sketchpad - Circles
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?
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