Waves are produced in the same medium. This means they have the same speed.
They also have the same period, implying that their wavelengths are also equal.
Since the waves start half a period apart, the phase difference between the sources is half a cycle, and remains constant since they are produced at the same frequency.
Point $C$ is five wavelengths from $A$, and four wavelengths from $B$, making the path difference one wavelength or a whole cycle. But after every single cycle, the two waves maintain a constant phase difference of $π$, leading to destructive interference.
