The point where all the medians meet
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the centroid is the intersection of medians
The centroid of a triangle is where the median of each side meet.
2/3 of the median is between the centroid and the vertex, 1/3 between the centroid and the side.
The centroid is the centre. How you find it depends on what information you have about the hypersphere.
Find the median of each side of the triangle. The centroid is where all three lines meet.