Centers of a Triangle Exploration
Use the check marks and move points A, B, and C to explore the different centers of a triangle.
1) What does a circumscribed circle look like? Sketch an example. Which special point creates the center of this circle? 2) What does an inscribed circle look like? Sketch an example. What special point creates the center of this circle? 3) The circumcenter is equidistant from what parts of the triangle? Explain using the term “radius.” 4) The incenter is equidistant from what parts of the triangle? Explain using the term “radius” 5) Match each type of segments to the special point it creates. Altitudes Incenter Medians Orthocenter Angle Bisectors Centroid Perpendicular Bisectors Circumcenter 6) What 3 special points are collinear? 7) What is the line called that are formed by 3 of the special point? 8) What kind of triangle causes all 4 points to become collinear? 9) Which special points sometimes are outside of the triangle? When does this happen? 10) What happens to the altitudes when constructed on a right triangle?