Diameter of Stars
There are few direct methods for determining the radii of stars. One of the most important uses eclipses of binary star systems. By carefully examining the light curve, it is possible to determine how long it takes one star to pass in front of the other. This can be used to infer the sizes of the stars.
At point 1 the eclipse starts and the light begins to decrease. At point 2 the eclipse becomes total and the light output is constant until point 3 where the smaller star begins to emerge and the light output begins to grow until finally at point 4 the eclipse is complete.
By similar reasoning, in the time from when the eclipse begins until it ends, the smaller star covers a distance equal to the diameter of the larger star. Thus, by carefully measuring this interval and multiplying by the velocity we can determine the diameter of the larger star.