Favorite problem: Serbian mathematical competition 2018 - Republic level, year 1, B category

My quick reasoning:

By law of sine, we have $\dfrac{a}{\sin{\theta}} = 2R$ or generally $R \propto \dfrac{a}{\sin{\theta}}$ , where $R$ is circumcircle's radius, $a$ is the longest side of triangle and $\theta$ corresponding angle. Taking the limit: $\lim_{\theta \to \pi}R = \lim_{\theta \to \pi}\dfrac{a}{\sin{\theta}} = \infty.$ So as $R$ goes to infinity, at some point it will certainly cross $2018$ . This is kind of intuitive since if $\theta = \pi$ then triangle comes down to a line, and circumcircle should pass through each of 3 points, which is impossible. This is true for all values of $a$ , until $a$ starts approaching zero, when the limit is not clear.

Am I right?