By definition, the line "'QS "'is the radical axis of the new circle with the green given circle, whereas the line "'P & prime; R & prime; "'is the radical axis of the new circle with the blue given circle.
42.
By definition, the line "'QS "'is the radical axis of the new circle with the green given circle, whereas the line "'P & prime; R & prime; "'is the radical axis of the new circle with the blue given circle.
43.
Since the distances from that pole point to the tangent points "'A "'1 and "'B "'1 are equal, this pole point must also lie on the radical axis " R " of the solution circles, by definition ( Figure 9 ).
44.
Referring to Figure 4, the radical axis ( red ) is perpendicular to the blue line segment joining the centers "'B "'and "'V "'of the two given circles, intersecting that line segment at a point "'K "'between the two circles.
45.
Laguerre ( 1882 ) applied the transformation to two cycles under the following conditions : Their radical axis is the axis of transformation, and their common tangents are parallel to two fixed directions of the half-lines that are transformed into themselves ( Laguerre called this specific method the " transformation by reciprocal half-lines " ).
46.
Alternatively, the orthogonal property of the two pencils follows from the defining property of the radical axis, that from any point " X " on the radical axis of a pencil " P " the lengths of the tangents from " X " to each circle in " P " are all equal.
47.
Alternatively, the orthogonal property of the two pencils follows from the defining property of the radical axis, that from any point " X " on the radical axis of a pencil " P " the lengths of the tangents from " X " to each circle in " P " are all equal.
48.
The radical axis of the two given circles is constructed; choosing two arbitrary points "'P "'and "'Q "'on this radical axis, two circles can be constructed that are centered on "'P "'and "'Q "'and that intersect the two given circles orthogonally.
49.
The radical axis of the two given circles is constructed; choosing two arbitrary points "'P "'and "'Q "'on this radical axis, two circles can be constructed that are centered on "'P "'and "'Q "'and that intersect the two given circles orthogonally.
50.
The studio was profiled in a 1940s-style mockumentary short, " Radical Axis Presents Radical Axis Presents ", that appeared as a Special Feature on the Aqua Teen Hunger Force Volume 6 DVD . Radical Axis has also been praised by comedian and " Freak Show " creator / writer, David Cross, who said, " Radical Axis is to animation what the Gutenberg Bible is to publishing.
