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Inversive geometry
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===== Point inside circle ===== To construct the inverse ''P'' of a point ''P{{'}}'' inside a circle ''Γ'': * Draw ray ''r'' from ''O'' (center of circle ''Γ'') through ''P{{'}}''. (Not labeled, it's the horizontal line) * Draw line ''s'' through ''P{{'}}'' perpendicular to ''r''. (Not labeled. It's the vertical line) * Let ''N'' be one of the points where ''Γ'' and ''s'' intersect. * Draw the segment ''ON''. * Draw line ''t'' through ''N'' perpendicular to ''ON''. * ''P'' is where ray ''r'' and line ''t'' intersect.
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