Pedal Circle
The pedal Circle of a point 
in a Triangle is the Circle through the feet of the perpendicularsfrom to the sides of the Triangle (the Circumcircle about the Pedal Triangle). When is on aside of the Triangle, the line between the two perpendiculars is called the Pedal Line. Given four points,no three of which are Collinear, then the four Pedal Circles of each point for theTriangle formed by the other three have a common point through which the Nine-Point Circles of the four Triangles pass. The radius of the pedal circle of a point is
(Johnson 1929, p. 141).See also Miquel Point, Nine-Point Circle, Pedal Triangle
References
Johnson, R. A. Modern Geometry: An Elementary Treatise on the Geometry of the Triangle and the Circle. Boston, MA: Houghton Mifflin, 1929.
- Logarithmic Spiral Radial Curve
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