The Center Of your Triangle Attention

By

Ryan Shannon

This is an investigation to the Incenter and Incircle of a Triangle.

Given:

-Point I is perpendicular to Line FH

-Point E is perpendicular to line FG

-Point J is perpendicular to line GH

The Incenter is the point of intersection of the perpendicular lines.

The Incircle has radius that is equal to the distance from the incenter to any point I, J, E

If the Triangle is equilateral then the radius will be equal to half the length of the legs of the triangle. The incenter is equidistant from all perpendicular points.

If we make triangle FHG an Acute Isosceles Triangle that is FH =HG and their angle is less than 90 degrees. The distance from I on FH to the incenter will be 1/4 the length of the Leg.

If we make triangle FHG an Obtuse Isosceles Triangle that is FH =HG and their angle is greater than 90 degrees. The distance from I on FH to the incenter will be 1/7 the length of the Leg.

For an animation to the Incenter and the Incircle Click image Above for the GSP 4.0 Animation File Animate Point G.