l m n P Circumcenter of a Triangle P
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The Circumcenter of a Triangle
Name _________________________________ Date ___________________ Period _______
When three or more lines intersect at one point, the lines are said to be concurrent.
m
n P
l
Circumcenter of a Triangle The point of concurrency of the perpendicular bisectors of a triangle. Y n l
P X
m
Z
Circumcenter of a Triangle The circumcenter is the center of the circle that is circumscribed around the triangle. Y
Point P is the center of the circle circumscribed around ∆XYZ
P
Point P is the circumcenter of ∆XYZ
Z
X
Circumcenter Theorem The circumcenter of a triangle is equidistant from all vertices of the triangle. Y
X
Point P is the center of the circle circumscribed around ∆XYZ
P
Point P is the circumcenter of ∆XYZ
Z
© iTutoring.com The Circumcenter of a Triangle Pg. 2
Circumcenter of a Triangle The circumcenter of a triangle can be inside, outside, or on the triangle.
B
B
P
P A
B
C
Point P, the circumcenter, is inside of ∆ABC
A
P C
Point P, the circumcenter, is on of ∆ABC
A
C
Point P, the circumcenter, is outside of ∆ABC
∆XYZ has vertices X(0,0), Y(4,0) and Z(0,-6). Find center and radius of the circle that can be circumscribed around ∆XYZ.
© iTutoring.com The Circumcenter of a Triangle Pg. 3
Circumcenter of a Triangle The point of concurrency of the perpendicular bisectors of a triangle. Y n l Point P is the center of the circle circumscribed around ∆XYZ
P
Point P is the circumcenter of ∆XYZ X
m
Z
The circumcenter of a triangle is equidistant from all vertices of the triangle.
© iTutoring.com The Circumcenter of a Triangle Pg. 4
The Circumcenter of a Triangle
Name _________________________________ Date ___________________ Period _______
When three or more lines intersect at one point, the lines are said to be concurrent.
m
n P
l
Circumcenter of a Triangle The point of concurrency of the perpendicular bisectors of a triangle. Y n l
P X
m
Z
Circumcenter of a Triangle The circumcenter is the center of the circle that is circumscribed around the triangle. Y
Point P is the center of the circle circumscribed around ∆XYZ
P
Point P is the circumcenter of ∆XYZ
Z
X
Circumcenter Theorem The circumcenter of a triangle is equidistant from all vertices of the triangle. Y
X
Point P is the center of the circle circumscribed around ∆XYZ
P
Point P is the circumcenter of ∆XYZ
Z
© iTutoring.com The Circumcenter of a Triangle Pg. 2
Circumcenter of a Triangle The circumcenter of a triangle can be inside, outside, or on the triangle.
B
B
P
P A
B
C
Point P, the circumcenter, is inside of ∆ABC
A
P C
Point P, the circumcenter, is on of ∆ABC
A
C
Point P, the circumcenter, is outside of ∆ABC
∆XYZ has vertices X(0,0), Y(4,0) and Z(0,-6). Find center and radius of the circle that can be circumscribed around ∆XYZ.
© iTutoring.com The Circumcenter of a Triangle Pg. 3
Circumcenter of a Triangle The point of concurrency of the perpendicular bisectors of a triangle. Y n l Point P is the center of the circle circumscribed around ∆XYZ
P
Point P is the circumcenter of ∆XYZ X
m
Z
The circumcenter of a triangle is equidistant from all vertices of the triangle.
© iTutoring.com The Circumcenter of a Triangle Pg. 4
