l= π/2
1) To find out the length of the arc BC with a central angle ∠BAC, we'll use the following formula:
[tex]l=\frac{\alpha}{360}\cdot2\pi r[/tex]
2) Now we can plug into that the given data, considering that ∠ BAC is a central angle then we can affirm:
[tex]m\widehat{BC}=m\angle BAC[/tex]
So we can plug into the formula below 45º as the angle of that arc, as it follows:
[tex]\begin{gathered} l=\frac{\alpha}{360}\cdot2\pi r \\ l=\frac{45}{360}\cdot2\pi\cdot2 \\ l=\frac{1}{2}\pi\text{ or }\frac{\pi}{2} \end{gathered}[/tex]
3) Hence, as we can see the answer is the l= π/2
