Problem #PRU-108604

Problems Geometry Plane geometry Triangles Relationship of side lengths and angles of a triangle. Solving triangles. Ceva's theorem and Menelaus's theorem Calculus Integral Existence of a definite integral Vectors Law of polygon of vectors Similar triangles

13–14 3.0

Problem

On the sides $A B$ , $B C$ and $A C$ of the triangle $A B C$ points $P$ , $M$ and $K$ are chosen so that the segments $A M$ , $B K$ and $C P$ intersect at one point and $\vec{A M} + \vec{B K} + \vec{C P} = 0$ Prove that $P$ , $M$ and $K$ are the midpoints of the sides of the triangle $A B C$ .

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