ill lie outside the circumscribed circle. This confirms that a pair of triangles satisfies the Delaunay condition.</p>
<p>$$
\alpha + \beta &lt; \pi \Rightarrow \sin(\alpha + \beta) &gt; 0
$$</p>
<p>$$
\sin(\alpha + \beta) = \sin(\alpha)\cos(\beta) + \cos(\alpha)\sin(\beta)
$$</p>
<p>Calculating \(\cos(\alpha)\) and \(\sin(\alpha)\):</p>
<p>$$
\cos(\alpha) = \frac{\vec{a} \cdot \vec{b}}{|a||b|} = \frac{a_{x}b_{x} + a_{y}b_{y}}{|a||b|}
$$</p>
<p>$$
\sin(\alpha) = \sqrt{1- \cos^2(\alpha)} = ... = \frac{|a_{x}