Let the triangle ABC be any triangle. Then if P is any point in the plane, then the triangle formed by constructing perpendiculars to the sides of ABC locate three points R,S, and T that are the intersections. Triangle RST is the Pedal Triangle for Pedal Point P.
RST triangle is the Pedal Triangle for Pedal Point P.
When P is external to the triangle ABC, P is always consistent with a vertex or external to the pedal triangle.
When P is internal to the triangle ABC, P is always internal to the pedal triangle.
If you would like to see different pedal triangles for ( P points outside the ABC triangle) click here
If you would like to see different pedal triangles for ( P points inside the ABC triangle) click here
If you would like to see different pedal triangles for ( P points over the ABC triangle) click here
The most interesting observation occured when we moved P point to a vertex, pedal triangle become a segment.
Investigation if pedal point P is the centroid of triangle ABC
a) The centroid of ABC triangle is inside of ABC triangle
b) The centroid of ABC triangle is outside of ABC triangle
Investigation if pedal point P is the orthocenter of triangle ABC
a) The orthocenter of ABC triangle is inside of ABC triangle
b) The orthocenter of ABC triangle is outside of ABC triangle
Investigation if pedal point P is on the nine-point circle of triangle ABC
a) if pedal point P is on the nine-point circle of triangle ABC
b) if pedal point P is on the nine-point circle center(N point) of triangle ABC