Applied Mechanics and Graphic Statics
A square hole is punched out of a circular lamina, the diagonal of the square being the radius of the circle. If ‘r’ is the radius of the circle, the C.G. of the remainder from the corner of the square on the circumference will be

[r (π + 0.25)]/(π + 0.5)
[r (π - 0.5)]/(π + 0.25)
[r (π - 0.25)]/(π - 0.5)
[r (π + 0.25)]/(π - 0.5)

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Applied Mechanics and Graphic Statics
The resolved part of the resultant of two forces inclined at an angle θ in a given direction is

Algebraic sum of the resolved parts of the forces in the direction
Difference of the forces multiplied by cosine θ°
Arithmetical sum of the resolved parts of the forces in the direction
Sum of the forces multiplied by the tangent θ°

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Applied Mechanics and Graphic Statics
Varingon’s theorem of moment’s states

Algebraic sum of the moments of the forces about any point in their plane, is equal to the moment of their resultant about that point
Arithmetical sum of the moments of two forces about any point, is equal to the moments of their resultant about that point
Arithmetical sum of the moments of the forces about any point in their plane, is equal to the moment of their resultant about that point
Algebraic sum of the moments of two forces about any point, is equal to the moment of their resultant about that point

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