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Using Varignon’s Theorem to show concurrency of coplanar forces in equilibrium

If a body is in equilibrium under the action of three non-parallel coplanar forces, the forces must be concurrent (Muncaster 1993 A Level Physics 4th edn (Cheltenham: Nelson Thornes) p 44, 45, 49; Goh 2018 Phys. Teach. 56 384). It is easy to show that they are concurrent when the forces meet at a point in the body (Muncaster 1993 A Level Physics 4th edn (Cheltenham: Nelson Thornes) p 44, 45, 49). However, in a situation that is easily found in common physics problems, the point of coincidence of the three lines of forces lie outside the object. It is our intention in this paper to illustrate to students how Varignon’s Theorem could be used to show that the forces must meet at a point even if the point lies outside the object when the three forces are in equilibrium.