5.4-5.5 Four Centers of Triangles

Define: CIRCUMCENTER OF A TRIANGLE

• 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 

Which point is equidistant from the vertices?

• Circumcenter
• Incenter
• Neither
• Bilateral

Which point is equidistant from the sides?

• Circumcenter
• Incenter
• Neither
• Bilateral

Name the point of concurrency shown.

• Circumcenter
• Incenter
• Supercenter
• Neither

Name the point of concurrency shown.

• Circumcenter
• Incenter
• Supercenter
• Neither

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

• DA
• AC
• PC
• PF

P is the incenter of triangle JKL. Find OP.

• 8

• 13

• 17

• 4

P is the incenter of triangle JKL. Find ML.

Hint: you will have to use pythagorean theorem

• 3.2

• 15.3

• 10.2

• 12.7

[Angle Bisectors and Incenter]
If m<BAC is 36°, what is m<PAC?

• 72°

• 48°

• 18°

• 36°