### Pedal Triangle

For any given triangle we define a pedal triangle in terms of a point
(P) and the triangle as follows. The pedal triangle is the triangle whose
vertices are the feet of the perpendiculars from the point to the sides
of the given triangle. The circle circumscribed about the pedal triangle
is called the pedal circle.

To observe a GSP sketch that illustrates the effect of both the shape
of triangle ABC and the position of the point p click
here.

If we allow the point P to lie on the circumference of a circle then the
feet of the perpendicular will be collinear and the line formed is called
the Simson line. To view the Simson line click
here.

The point (P) is a specific example of a series of points known as the Miquel
point.

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