Constructions using Geometer’s Sketchpad

I. Incenter of a triangle (refer to page 547)

1. Construct a triangle (Click on the symbol and then draw the sides by holding the mouse button in the sketch and dragging to the desired location)

2. Construct each angle bisector:

1. Click on the symbol

2. Hold down the Shift key
3. Click on points A, then B, then C.
4. Go to Construct at the top of the page
5. Choose Angle bisector (if not available, click in an open area and try steps a, b, c again)
6. Repeat steps a to e, except in step c: click on point B first, then C, then A.
7. Repeat again, except in step c: click on C first then A, then B

3. Construct a circle inside the triangle

a. Click on one of the angle bisectors

b. Go to Construct at the top of the page

c. Choose Point on object

d. Click on the point and slide it to the intersection of the 3 angle bisectors

e. Click on the symbol

f. Click on the intersection point and drag out to make a circle that just touches each side of the triangle (the triangle is tangent to the circle).

II. Circumcenter of a Triangle

1. Construct a triangle

2. Construct each perpendicular bisector:

1. Click on the symbol

2. Click on one side of the triangle
3. Go to Construct at the top of the page
4. Choose Point at Midpoint
5. Hold down shift and click on that same side again
6. Go to Construct and Choose Perpendicular Line
7. Repeat with the other 2 sides of the triangle

3. Construct a circle outside the triangle

a. Click on one of the perpendicular bisectors

b. Go to Construct at the top of the page

c. Choose Point on object

d. Click on the point and slide it to the intersection of the 3 perpendicular bisectors

e. Click on the symbol

f. Click on the intersection point and drag out to make a circle that just touches each vertex of the triangle.