Circle J is centered on the origin. If the equation for a chord within

The official solution by Veritas is this one:

"The key to solving this problem is recognizing that to find the circumference you have to know the radius. And since the problem provides you with the center (0, 0) and tells you that the chord intersects the circle at the x-axis, it gives you a roadmap to find exactly that radius: if you can find the second coordinate of that point where the chord intersects the circle (you know that it intersects at the x-axis, which is where y = 0) you have the radius.

Since at that point y = 0, then plug that into the equation for the chord. That wipes out the √3y term, making the equation just x = 5. So that point is (5, 0), meaning that the radius of the circle is 5, and the circumference is then 10π".

Evrything sounds good, but I need to ask about one thing. Why are we assuming that the x in the equation of the line for the chord is the same x as in the point (0,0)? Is this a rule I don't know?