CONCURRENCY TIMES

TABLE OF CONTENtS

• Definitions
• Incenter
• Circumcenter
• Centroid
• Examples in the real world

DEFINITIONS

PROPERTIES OF INCENTER

• Formed by the intersection angle bisector.
• Always located within the triangle.
• The segments are not always passing through midpoint of opposite sides.
• Segments are not always perpendicular to opposite sides.
• Equidistant to each side.

PROPERTIES OF CIRCUMCENTER

• Formed by the intersection of perpendicular bisectors.
• Located inside on acute, outside on obtuse, and on the triangle with right.
• Segments are not always angle bisectors.
• Circumcenter is equidistant to each vertex.

PROPERTIES OF CENTROID

• Formed by the intersections of medians.
• Always located inside the triangle.
• Segments are not always angle bisectors.
• Segments are not always passing through 90* to opposite sides.
• Cuts the median in a two to one ratio.

EXAMPLES

REAL WORLD EXAMPLES

LOCATIONS

• Incenter : always inside
• Circumcenter : acute ; inside , obtuse ; outside , right ; on the triangle
• Centroid : always inside
• Orthocenter : acute ; inside , obtuse ; outside , right ; on the vertex