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8.4.3 Orthogonal Circles An interesting situation to consider is when circles (or lines, or lines and circles) intersect at 90. In any of these cases, the two figures are called orthogonal. In figure 8.9 the circle in the center is surrounded by a set of circles that are orthogonal to it. Since angles are preserved under inversion, what happens if a circle is inverted through another circle to which it is orthogonal? The answer is that the circle is inverted into itself. To see why, remember that the circle of inversion is unchanged by the inversion. The circle orthogonal to it is mapped to a circle that meets it at the same points, and remains orthogonal. Therefore it must be mapped to the same circle. (Note that this does not mean that the points are not moved by the inversion—the ones outside are mapped to points inside and vice-versa, but every point on that circle is inverted to another point on the same circle.)

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  • 27qtbb
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Could you send me the reference: Title, book, journal, etc and chapter,Date, if any? Especially、 the subject? すこし時間がかかるでしょうけど、もしおそくなければ是非、挑戦したいです。 よろしく

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