8/28/2023 0 Comments Line of reflection compass![]() ![]() Still, the standardĬonstruction is interesting. Our construction using just a compass will come later. Straightedge, so we won't be able to use it. The standard construction to invert a point in a circle uses both compass and Otherwise said, it is an operation that when done twice yields the identity operation.Īlgebraically, this observation is the identity ( B C) C =Īlso note that a point P is its own inverse, that is, P C = P, if and only if it lies on the circumference of the circle. That is, application of inversion in the same circle a second Note that inversion in a circle is an involution. Is a straight line, then B L is the figure that results from reflecting B across So, if B is any plain geometric figure, and L We'll also use this notation for reflecting across a straight line. We'll use the notation B C for the result of inverting B in the circle C. Read " P C" as " P throughĬ." More generally, when B is any plane geometric figure (point, line, circle, etc.) and C is a circle, ![]() We'll use the notation P C to indicate the inverse point P'. O of the circle, we'll add a point to the plane, and let O and be inverses of each other. In order to cover the special case that occurs when P is the center (extended in the direction of P if needed) so that the proportion For each point P other than theĬenter O, the point inverse to P in the circle O is that point P' on the line OP Of course, we need a definition.įix a circle with center O and radius OA = r. Summary of inversionWe don't need all the properties of inverion in a circle for this ![]()
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