Answer Happy

Use a circle tool in GeoGebra to create a circle K with center q and radius R, and let Ik denote inversion (or reflection) across K. (a) Use the line tool to create a line L, then the “reflect across circle” tool to find the reflection L' = IK(L) of L across K. Now use the “Move” tool to move L until it becomes an invariant curve of IK. Give a one-sentence description of the invariant lines of IK. (b) Use a circle tool to create a circle C, then the “reflect across circle” tool to find the reflection C' = IK(C) of C across K. Now use the “Move” tool to move C until it becomes an invariant curve of IK. Find five different invariant circles of IK. Do they have anything in common? Describe, in a sentence or two, what you notice or don't notice about invariant circles of IK. =