Theorem of Apollonius

Theorem of Apollonius states that in a triangle, if you choose a point on one side and draw a line segment to the opposite vertex, the sum of the squares of the lengths from that point to the two other vertices equals twice the square of the segment connecting the point to the side, plus twice the square of the segment connecting the point to the vertex. It provides a specific relationship between the lengths within a triangle, helping analyze geometric properties and relationships among points, lines, and distances in the shape.