In the diagram below, chords $\overline{AB}$ and $\overline{CD}$ are perpendicular, and meet at $X.$ Find the diameter of the circle.
The diameter is 4.
Any perpendicular lines, assuming that they connect to both ends of a cricle, will meet at the center, which is X in this case. Now that we know X is the center of the circle and that 2 is from D to X, we can conclude that the radius is 2. Therefore, the diameter is 4.