Incenter of a Triangle (Braak)
Incenter of a triangle
1. Create an angle bisector for each angle of the triangle. (Use angle bisector tool- 4th menu from left)
* Using "angle bisector" tool click the three points that form the angle (For instance: For the angle at <CAB you would click "C" then "A" then B"
2. Note all the angle bisectors intersect. Label the intersection point D
3. Use the "Circle with a center through a point" tool -(6th menu from left) to inscribe a circle. The circle should meet the sides of each segment of the triangle.
Incenter
What kinds of lines create the incenter of a circle?
Are the angle bisectors equal distance from the center to each vertex angle?
Below is what you created, but I have hidden the angle bisectors.
1. Find the perpendicular lines from the center to the sides of the triangle. Click "perpendicular line" tool Click the center of the circle, then a side of the triangle. Do this to create all three perpendicular bisectors.
2.) Label the points of intersection F, G, H
Length of Perpendicular Bisectors
Use the "distance or length" tool - (8th menu from the left) and measure the lengths of DF, DG, DH. What do you notice about those lengths?