lukester wrote:If circle A has 3 times the area of circle B, and circle B has one-sixth of the area of square WXYZ, what is the ratio of the area of a circle inscribed within WXYZ to that of the area of circle A?

A) π/12
B) π/6
C) π/2
D) 2/Ï€
E) √12π

The question gives us the following relations:

• 1. Area of circle A = 3*(Area of circle B)
  2. Area of circle B = (Area of square WXYZ)/6

And asks for the ratio of the area of a circle inscribed within WXYZ to that of the area of circle A.

Now side of square WXYZ = Diameter of the circle inscribed in it = a (Say)

Area of square WXYZ = a²
Area of inscribed circle = π(a/2)² = (π/4)*a² = (π/4)*(Area of square WXYZ)

Now replace the given information one by one,
Area of inscribed circle = (Ï€/4)*(Area of square WXYZ) = (Ï€/4)*(6*(Area of circle B)) = (Ï€/4)*(6*(Area of circle A)/3) = (Ï€/2)*(Area of circle A)

Therefore the required ratio = π/2

The correct answer is C.