Construct the centroid (medians), circumcenter (perpendicular bisectors), and orthocenter of a right triangle (altitudes).
The three angle bisectors of a triangle are concurrent in a point equidistant from its sides. The incenter of a triangle is the point at which the triangle's angle bisectors intersect. The incenter is always inside the triangle.
The point where the three perpendicular bisectors meet is the circumcenter of a triangle. It is the circumcenter of the circle encircling the triangle, equidistant from the triangle's three vertices.
The incenter exists crucial for angle bisectors; the orthocenter is important for perpendicular bisectors; the circumcenter is important for altitudes; and the centroid is important for medians.
Construct a right triangle's centroid (medians), circumcenter (perpendicular bisectors), and orthocenter (altitudes).
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