Simson Line

by Kaori Tabeta

Find all conditions in which the three vertices of the Pedal triangle are colinear (that is, it is a degenerate triangle). Like as following.

This line segment is called the Simson Line.

Try to fInd all condicions to move the pedal point P as following.

However it seems that there are more conditions when the pedal triangle SRT is a degenerate triangle.For example, When the vertex T move on the side AC the conditions are as following.

Trace the point P and move P the triangle STR will be Simson as following.

It looks like circle and through three vertexes, in the other word it looks like circumcircle. Then the pedal point P moves on the circumcircle as following. Click here for GSP file of circumcircle.

When pedal point P move on the circumcircle of original triangle ABC , pedal triangle STR is SImon Line.


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