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Which two points of concurrency always remain inside the triangle, and why?

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The point of concurrency is the point where three or more lines, segments, or rays intersect forming a point. Out of the four namely the Centroid, Incenter, Circumcenter, and Orthocenter, only the Centroid and Incenter is always located inside the triangle.

Centroid: where the medians intersect

Incenter: where the angle bisectors intersect

User Masterxilo
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