Lamis theorem proof
If three forces acting on a particle keep it in equilibrium, each is proportional to the sine of the angle between the other two.
Thus if the forces are P, Q and R and α, β, γ be the angles between Q, R; R, P; and P, Q respectively then if the forces are in equilibrium, we have
Example: Forces P, Q and R acting along OA, OB and OC, where O is the circumcentre of the triangle ABC are in equilibrium. Show that
Detail Explanation : ∠ BOC = 2A, ∠COA = 2B, ∠AOB = 2C
Applying Lami's Theorem , we get
Apply sine rule and cosine rule to get