Theorems on special lines in triangles

The three medians in a triangle pass through one point. This point is called the centroid of a triangle.

The centroid divides each median in the ration 2:1

All points of the perpendicular bisector of a line segment AB have equal distances to A and B

The perpendicular bisectors of the three sides of a triangle pass through one point. This point is the centre of the circumscribed circle of that triangle.

All points of the bisector of an angle have equal distances to the legs of that angle.

The bisectors of the three angles in a triangle pass through one point. This point is the centre of the inscribed circle of the triangle.