CK-12 Geometry-Concepts

http://www.ck12.org Chapter 5. Relationships with Triangles

The circumcenter is the center of a circle that passes through all the vertices of the triangle. We say that this circle
circumscribesthe triangle. This means thatthe circumcenter is equidistant to the vertices.

Concurrency of Perpendicular Bisectors Theorem:The perpendicular bisectors of the sides of a triangle intersect
in a point that is equidistant from the vertices.

IfPC,QC, andRCare perpendicular bisectors, thenLC=MC=OC.

Example A

Findxand the length of each segment.

From the markings, we know that

←→

W Xis the perpendicular bisector ofXY. Therefore, we can use the Perpendicular
Bisector Theorem to conclude thatW Z=WY. Write an equation.

2 x+ 11 = 4 x− 5

16 = 2 x

8 =x

To find the length ofW ZandWY, substitute 8 into either expression, 2( 8 )+ 11 = 16 + 11 =27.