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CONCURRENT LINES. Three or more lines that intersect at a common point. POINT OF CONCURRENCY. The point at which 3 or more lines intersect. Point of concurrency. CIRCUMCENTER. Point of concurrency for the perpendicular bisectors of a triangle. circumcenter. Circumscribed circle.

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Point of concurrency
POINTOFCONCURRENCY






Concurrent lines

circumcenter triangle



Concurrent lines
A circle that is drawn around a triangle so that each vertex of the triangle is a point on the circle


Circumcenter theorem
Circumcenter Theorem of the triangle is a point on the circle

The circumcenter of a triangle is located equidistant from each vertex of the triangle.

BO=AO=CO


Incenter
INCENTER of the triangle is a point on the circle


Point of concurrency for the angle bisectors of a triangle
Point of concurrency for the angle bisectors of a triangle of the triangle is a point on the circle


Concurrent lines

incenter of the triangle is a point on the circle

50

50


Inscribed circle
Inscribed circle of the triangle is a point on the circle


Concurrent lines
A circle using the of the triangle is a point on the circleincenter of a triangle as its center, and is drawn so that each side of the triangle touches the circle in one point


Incenter theorem
Incenter Theorem of the triangle is a point on the circle

  • The incenter of a triangle is equidistant from each side of the triangle.

AI = BI = CI

A

I

B

C


Median
MEDIAN of the triangle is a point on the circle



Concurrent lines

4 opposite side of a triangle

4


Centroid
CENTROID opposite side of a triangle



Concurrent lines

centroid opposite side of a triangle


Altitude
ALTITUDE opposite side of a triangle



Orthocenter
ORTHOCENTER to the opposite side



Concurrent lines

orthocenter to the opposite side