find the inversion of a point, line, or circle with respect to a given circle
inversion(Q, P, c)
the name of the object to be created
point, line, or circle
If P is a point that is not the same as the center O of circle c⁡r, the inverse of P in, or with respect to, circle c⁡r is the point Q lying on the line OP such that SensedMagnitude⁡OP⁢SensedMagnitude⁡OQ=r2.
If P is a line passing through center O of circle c⁡r, the inverse of P is P itself. In case P is a line not passing through center O of circle c⁡r, the inverse of P is a circle Q passing though O perpendicular to P
If P is a circle passing through the center O of circle c⁡r, the inverse of P is a straight line Q not passing through O and perpendicular to the diameter of c⁡r through O. In case P is a line not passing through the center O of circle c⁡r, the inverse of P is a circle Q not passing through O and homothetic to circle c⁡r with O as center of homothety.
For a detailed description of Q the object created, use the routine detail (i.e., detail(Q);)
The command with(geometry,inversion) allows the use of the abbreviated form of this command.
Inversion of a point with respect to a circle
Inversion of a line with respect to a circle
inversion of a circle with respect to a circle
name of the objectc1form of the objectcircle2dname of the centercenter_c1coordinates of the center0,0radius of the circle16equation of the circlex2+y2−16=0,name of the objectc2form of the objectcircle2dname of the centercenter_c2coordinates of the center3,0radius of the circle36equation of the circlex2+y2−6⁢x−27=0,name of the objectc3form of the objectcircle2dname of the centercenter_c3coordinates of the center1297,0radius of the circle−36⁢167equation of the circle491296⁢x2−301216⁢x−455144+491296⁢y2=0
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