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What is the point of the concurrency called?


Asked by Scarlet Bravo on Dec 01, 2021 FAQ



The point of concurrency of angular bisectors is called incenter of the triangle . If we draw a circle taking the incenter as the centre and the distance from the incenter to any side of the triangle as the radius then we get a circle which touches all the sides of the triangle which is known as the incircle.
Keeping this in consideration,
A point of concurrency is a single point shared by three or more lines. Constructed lines in the interior of triangles are a great place to find points of concurrency. When you construct things like medians, perpendicular bisectors, angle bisectors, or altitudes in a triangle, you create a point of concurrency for each one.
Moreover, Point of Concurrency that is the midpoint of the hypotenuse of a right triangle Circumcenter Point of Concurrency that is the vertex of the right angle in a right triangle Orthocenter Point of Concurrency outside on an obtuse triangle and opposite the obtuse angle Circumcenter
Next,
Construct three perpendicular bisectors and they will cross each other at the point of concurrency called the circumcenter. A circumcenter is the center of a circle passing through all three vertices of the triangle. Such a circle is called a circumcircle.
Thereof,
A point of concurrency is where three or more lines intersect in one place. Incredibly, the three angle bisectors, medians, perpendicular bisectors, and altitudes are concurrent in every triangle. So none of these lines are concurrent.