Circumcenter and Incenter

Circumcenter and Incenter

By Ryan Kripp

​Concurrent Lines

• ​Three or more lines that intersect at exactly one point.

• ​

• ​Point of concurrency - the point of intersection of three or more lines.

​What is a CIRCUMCENTER?

The point of concurrency created by the 3 perpendicular bisectors.

​

​Notice: Each vertex of the triangle is EQUIDISTANT from the circumcenter.

​

Why is that?! They are the RADIUS of the outside circle!

​What is an INCENTER?

​

The point of concurrency created by the 3 angle bisectors.

​​

​They all meet at the INCENTER.

​

The Incenter is EQUIDISTANT from the sides of the Triangle

​

​Notice: The circle is INside.

Multiple Choice

The CIRCUMCENTER is the intersection of which special segments?

• Angle Bisectors

• Perpendicular Bisectors

• Medians

• Altitudes

Multiple Choice

The INCENTER is the intersection of which special segments?

• Angle Bisectors

• Perpendicular Bisectors

• Medians

• Altitudes

Multiple Choice

Which center of a triangle is shown in the picture below?

• Circumcenter

• Orthocenter

• Incenter

• Centroid

Multiple Choice

Which center of a triangle is shown in the picture below?

• Circumcenter

• Orthocenter

• Incenter

• Centroid

Multiple Choice

[Angle Bisectors and Incenter]:
If PX is 5, what is PZ?

• 20
• 10
• 5
• 15

Multiple Choice

[Perpendicular Bisectors and Circumcenter]
If AF is 6, what is AC?

• 6
• 10
• 16
• 12

Multiple Choice

Find the value of x

• x=28
• x=14
• x=23
• x=46

Multiple Choice

Point O is the circumcenter of the triangle. Find OB

• OB = 4
• OB = 6
• OB = 5.1
• Not enough information

Multiple Choice

Which point is equidistant from the vertices?

• Circumcenter
• Incenter
• Neither
• Bilateral

Multiple Choice

Name the point of concurrency shown.

• Circumcenter
• Incenter
• Supercenter
• Neither

Multiple Choice

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

• DA
• AC
• PC
• PF

Multiple Choice

P is the incenter of triangle JKL. Find ML.

Hint: you will have to use pythagorean theorem

• 8.95

• 9.35

• 10.25

• 12.65

Multiple Choice

P is the incenter of triangle JKL. Find OP.

• 8

• 13

• 17

• 4