5.3 Task - Circumcenter & Incenter

Circumcenter

Create an acute triangle labeled ABC.
Construct the perpendicular bisector of side AB and the point of their intersection labeled point D.
Construct the perpendicular bisector of side BC and the point of their intersection labeled point E.
Construct the perpendicular bisector of side AC and the point of their intersection labeled point F.
Create the point of intersection of the three perpendicular bisectors, label point G.
Hide the perpendicular bisectors.
Create segments from point G to each of the vertices: A, B, and C.
Measure and show the lengths of AG, BG, and CG.
Measure and show the lengths of AD, BD, BE, CE, AF, CF.

Create acute triangle labeled ABC.
Construct the angle bisectors of all three angles.
Create the point of intersection of the angle bisectors labeled point D.
Construct a line perpendicular to point D through side AB. Construct point E at the intersection.
Construct a line perpendicular to point D through side BC. Construct point F at the intersection.
Construct a line perpendicular to point D through side AC. Construct point G at the intersection.
Construct segments connecting point D to points E, F, and G.
Hide the angle bisectors.
Show the measures of the distances from the incenter, D to each side of the triangle: DE, DF, DG.
Show the measures of the distances from each vertex to the points of intersection of the perpendicular segments: AE & AG, BE & BF, CF & CG.