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 where the circle touches it. Do this to create all three perpendicular lines from the center to the side.
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?