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.
Incenter
- 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.