Answer in Brief

state and prove varigon’s theorem.

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#### Solution

ΣMAF= ΣMAR

Proof:

Let P and Q be two concurrent forces at O,making angle θ1 and θ2 with the X-axis

Let R be the resultant making an angle θ with X axis

Let A be a point on the Y-axis about which we shall find the moments of P and Q and also of resultant R.

Let d1,d2 and d be the moment arm of P,Q and R from moment centre A

The x component of forces P,Q and R are Px,Qx and Rx

∴ MAP = P x d1 ……..(1)

∴ MAQ = Q x d2 ……..(2)

∴ MAR = R x d

=R( OA.cosθ )

=OA.Rx

Adding (1) and (2)

∴ MAP+MAQ=Pd1+Qd2

ΣMAF = P x OAcosθ1 + Q x OAcos θ2

=OA.Px+OA.Qx (as Px=P.cosθ1 and Qx=Qcosθ2)

=OA(Px+Qx)

∴ ΣMAF = OA(Rx) ……..(3)

From (4) and (3)

ΣMAF= ΣMA

Thus,Varigon’s theorem is proved

Concept: Varignon’s Theorem

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