Arcs and pi, my oh my!

Consider a circle with center A, points B, C, and D on its circumference, and radius $r$ . $l\widehat{BCD}=4r$ . $m\widehat{BCD}=\frac{a}{b}$ , where one of these terms ( $a$ or $b$ ) is a natural number under 823, and the other is an irrational number.

$\left \lfloor{b}\right \rfloor=y$

$\left \lceil{b}\right \rceil=z$

$\frac{az}{y}-57=x$

What is the value of $x$ ?