# Arcs and pi, my oh my!

Geometry Level pending

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 $$x$$?

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