Question

An arbelos is the region bordered by three mutually tangent circles with co-linear centers. See shaded region in the figure. If the area of this region is 42π and the radii of the two smaller circles have a ratio of 2 : 3. What is the radius of the largest circle(x)?

• A.
  
• B.
  
• C.
  
• D.
  

Answer 1

The correct option is B

Let the radii of the two smaller circles be 2y and 3y respectively. This makes the radius of the larger circle 5y. We are told that the area is 42π, so we have

42$\pi$ = $\frac{1}{2}$($\pi (5y{)}^2-\pi (3y{)}^2-\pi (2y{)}^2$),

y = $\sqrt{7}$.
But x = 5y; So, x = $5\sqrt{7}$.