Multiple choice

Two intersecting circles have their radii $1$ and $\sqrt { 3 } $ meters. The distance between their centres is $2$ meters. Then the overlapping area in sq. meters is

  1. $\dfrac { 19\pi +6\sqrt { 3 } }{ 6 } $
  2. $\dfrac { 5\pi +6\sqrt { 3 } }{ 6 } $
  3. $\dfrac { \pi}{ 6 } $
  4. $\dfrac { 5\pi -6\sqrt { 3 } }{ 6 } $
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D Correct answer
Explanation

The area of intersection of two circles with radii r1, r2 and distance d is calculated using the formula for circular segments. For r1=1, r2=sqrt(3), d=2, the circles are orthogonal or intersect at specific angles. The calculation yields (5pi - 6sqrt(3))/6.

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