Hello, loizoud94!
Two parallel chords are 2cm from the centre of a circle of radius 4cm.
Calculate the area between them. Code:
* * *
*::::::::::*
*::::::::::::::*
A*    +    *B
* *
* * 120°* *
* *O *
*  *

C*    +    *D
*::::::::::::::*
*::::::::::*
* * *
The area of the circle is: .$\displaystyle \pi(4^2) \:=\:16\pi $ cm².
The area between the chords is:
. . the area of the circle minus the area of the two shaded segments.
We find that the sector has a central angle of 120°.
Hence, the area of the sector is: .$\displaystyle \tfrac{1}{3}\pi r^2 \:=\:\tfrac{16}{3}\pi$
The area of $\displaystyle \Delta AOB$ is: .$\displaystyle \tfrac{1}{2}(4)(4)\sin120^o \:=\:4\sqrt{3} $
. . Hence, the area of a segment is: .$\displaystyle \tfrac{16}{3}\pi  4\sqrt{3}$
The area betwen the chords is: .$\displaystyle A \;=\;16\pi  2\left(\tfrac{16}{3}\pi  4\sqrt{3}\right)$
Therefore: .$\displaystyle A \;=\;\tfrac{16}{3}\pi + 8\sqrt{3}$ cm²