Circumcenters and Incenters

Which point is equidistant from the vertices?

• Circumcenter

• Incenter

• Neither

• Bilateral

Point P is the circumcenter, which segment is equal to PB

• DA

• AC

• PC

• PF

Define: CIRCUMCENTER OF A TRAINGLE

• the intersection point of the three perpendicular bisectors of a triangle 

• when a circle passes through the three vertices of a triangle 

• the point of intersection of three or more lines 

• the intersection point of the three angle bisectors of a triangle 

Define: INCENTER OF A TRIANGLE

• the intersection point of the three angle bisectors of a triangle 

• when three or more lines intersect at a single point 

• the intersection point of the three perpendicular bisectors of a triangle 

• the point of intersection of three or more lines 

Point T is the incenter. Find the length of TU.

Which point is equidistant from the vertices? (a)   Which point is equidistant from the sides?​ (b)  

• Circumcenter

• Incenter

• Centroid

• Orthocenter

What is the special property for circumcenters?

• The circumcenter is equally distant to the midpoint of the sides of the triangle.

• The circumcenter is equally distant to the vertices.

Point G is the incenter. What is the length of BG?

Which point is equidistant from the vertices? (a)   Which point is equidistant from the sides?​ (b)  

• Circumcenter

• Incenter

• Centroid

• Orthocenter

P is the incenter. Which segment lengths are equal?