Why the path of the Moving Point is a segment

A triangle with angle C=90 degree, Point A, B move along the Y-axis and
X- axis.
Why the path of the Point C is a segment.
How to proof it ?
You may visit the web below to see the animation written in java
program.
(Drag Point G around the circle, you will see the moving path.)
http://twww.jhsh.tpc.edu.tw/~jojoba26/triangle.htm

thanks

.

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