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164 Geometry
lengths of the corresponding segments. If k=1, then the
lengths CA and CA’ are reciprocals.
Suppose you wish to find the inversion of a circle (GC) with a
point on the circle (GD) as center.
1. Tap and select More > Inversion.
2. Tap the point that is to be the center (GD) of the inversion
circle and press
E.
3. Enter the inversion
ratio—use the default
value of 1—and press
E.
4. Tap on the circle( GC)
and press
E.
You will see that the
inversion is a line.
Reciprocation A reciprocation is a special case of inversion involving circles.
A reciprocation with respect to a circle transforms each point
in the plane into its polar line. Conversely, the reciprocation
with respect to a circle maps each line in the plane into its
pole.
1. Tap and select More > Reciprocation.
2. Tap the circle and press
E.
3. Tap a point and press
E to see its polar
line.
4. Tap a line and press
E to see its pole.
In the illustration to the
right, point K is the
reciprocation of line DE
(G) and Line I (at the bottom of the display) is the
reciprocation of point H.