Skip to content / Đến nội dung
ThichHocToan.com

SMO 2011 Junior Round 1 Question 6

SMO · SMO 2011 Junior Round 1

Question 6

Consider the following egg shaped curve. $ABCD$ is a circle of radius 1 centred at $O$. The arc $\widehat{AE}$ is centred at $C$, $\widehat{CF}$ is centred at $A$ and $\widehat{EF}$ is centred at $D$.

Question illustration

What is the area of the region enclosed by the egg shaped curve?
  1. $(3-\sqrt2)\pi-1$
  2. $(3-\sqrt2)\pi$
  3. $(3+\sqrt2)\pi+1$
  4. $(3-2\sqrt2)\pi$
  5. $(3-2\sqrt2)\pi+1$