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- Radical_axis abstract "The radical axis (or power line) of two circles is the locus of points at which tangents drawn to both circles have the same length. For any point P on the radical axis, there is a unique circle centered on P that intersects both circles at right angles (orthogonally); conversely, the center of any circle that cuts both circles orthogonally must lie on the radical axis. In technical language, each point P on the radical axis has the same power with respect to both circleswhere r1 and r2 are the radii of the two circles, d1 and d2 are distances from P to the centers of the two circles, and R is the radius of the unique orthogonal circle centered on P.The radical axis is always a straight line and always perpendicular to the line connecting the centers of the circles, albeit closer to the circumference of the larger circle. If the circles intersect, the radical axis is the line passing through the intersection points; similarly, if the circles are tangent, the radical axis is simply the common tangent. In general, two disjoint, non-concentric circles can be aligned with the circles of bipolar coordinates; in that case, the radical axis is simply the y-axis; every circle on that axis that passes through the two foci intersect the two circles orthogonally. Thus, two radii of such a circle are tangent to both circles, satisfying the definition of the radical axis. The collection of all circles with the same radical axis and with centers on the same line is known as a pencil of coaxal circles.".
- Radical_axis thumbnail Radical_axis_orthogonal_circles.svg?width=300.
- Radical_axis wikiPageExternalLink IncircleInSegment1.shtml.
- Radical_axis wikiPageID "2093844".
- Radical_axis wikiPageRevisionID "605859066".
- Radical_axis hasPhotoCollection Radical_axis.
- Radical_axis subject Category:Analytic_geometry.
- Radical_axis subject Category:Circles.
- Radical_axis subject Category:Elementary_geometry.
- Radical_axis type Abstraction100002137.
- Radical_axis type Attribute100024264.
- Radical_axis type Circle113873502.
- Radical_axis type Circles.
- Radical_axis type ConicSection113872975.
- Radical_axis type Ellipse113878306.
- Radical_axis type Figure113862780.
- Radical_axis type PlaneFigure113863186.
- Radical_axis type Shape100027807.
- Radical_axis comment "The radical axis (or power line) of two circles is the locus of points at which tangents drawn to both circles have the same length. For any point P on the radical axis, there is a unique circle centered on P that intersects both circles at right angles (orthogonally); conversely, the center of any circle that cuts both circles orthogonally must lie on the radical axis.".
- Radical_axis label "Eje radical".
- Radical_axis label "Machtlijn".
- Radical_axis label "Potenzgerade".
- Radical_axis label "Prosta potęgowa".
- Radical_axis label "Radical axis".
- Radical_axis label "Радикальная ось двух окружностей".
- Radical_axis sameAs Potenzgerade.
- Radical_axis sameAs Eje_radical.
- Radical_axis sameAs Potentzia-ardatz.
- Radical_axis sameAs Machtlijn.
- Radical_axis sameAs Prosta_potęgowa.
- Radical_axis sameAs m.06lq5r.
- Radical_axis sameAs Q2106473.
- Radical_axis sameAs Q2106473.
- Radical_axis sameAs Radical_axis.
- Radical_axis wasDerivedFrom Radical_axis?oldid=605859066.
- Radical_axis depiction Radical_axis_orthogonal_circles.svg.
- Radical_axis isPrimaryTopicOf Radical_axis.
