Circle Problem

Let the angle that extend the chord be $\theta$ , then:

$\begin{cases} \theta r = 16.76 \\ 2 r \sin {\frac{\theta}{2}} = 15.43 \end{cases}$

Dividing the two equations, we have:

$\dfrac {2 \sin {\frac {\theta}{2}}} {\theta} = \dfrac {15.43}{16.76} \quad \Rightarrow \sin {\frac {\theta}{2}} = 0.460322196 \space \theta$

We can use Newton's method to find $\theta$ . I implemented it with a spreadsheet (see below).

We find that $\theta = 1.396994733$ rad $\quad \Rightarrow r = \dfrac {16.76}{\theta} = \dfrac {16.76}{1.396994733} = 11.99718195 \approx \boxed{12}$