Assignment 9:

Serkan Hekimoglu and Jamie Parker

EMAT 6680

University of Georgia (Dr.Wilson)

Pedal Triangle

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.

Figure 1: Construction of Pedal Triangle

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.

Figure 2: P point is on A point

Investigation if pedal point P is the centroid of triangle ABC

a) The centroid of ABC triangle is inside of ABC triangle

Figure 3: Pedal point P is centroid of ABC triangle

b) The centroid of ABC triangle is outside of ABC triangle

Figure 4: 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

Figure 5: Pedal point P is orthocenter of ABC triangle

b) The orthocenter of ABC triangle is outside of ABC triangle

Figure 5: Pedal point P is orthocenter of ABC triangle(orthocenter is outside the 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

back to bio page