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.