Perpendicular Bisector – a line, segment, or ray that bisects a line segment and is perpendicular to that segment Circumcenter – the point of concurrency where the three perpendicular bisectors of a triangle intersect Construct a circumcenter 1.) To find Geometer’s Sketchpad -­‐ click the magnifying glass in the top right corner of the screen and search for: GSP (click on the top hit – the yellow diamond with the shapes) 2.) Click the segment button
on the toolbar. 3.) Click to make a line segment. Start another line segment at one of the end points (the point will become outlined in red when you are on the point) 4.) Click to make a third line segment closing the triangle. 5.) Click the cursor button on the toolbar and click in the white space to deselect all points and segments. 6.) Click on a side of your triangle and choose Construct > Midpoint. Deselect all points and segments. 7.) Click on the side and the midpoint you just constructed so that both are highlighted in red and choose Construct > Perpendicular Line. You have constructed your first perpendicular bisector. 8.) Repeat steps 6 and 7 for the other two sides of the triangle. Deselect all points and segments. 9.) Highlight two of your perpendicular bisectors and choose Construct > Intersection. The point you just constructed is your circumcenter. Deselect all points and segments. 10.)Click the circle button on the toolbar. Click on your circumcenter to center your circle there. Stretch the circle so that it intersects each vertex of your triangle.