Quote: ''To get the size of a star usually involves estimating the distance to the star. Stars that are not too too far away can have their distances measured using parallax. As the earth moves around the sun, we see the stars from a different vantage point every night. Observations made six months apart have the biggest difference in vantage point. If we compare where we see a nearby star, as seen in a background of very faraway stars, at one observation and six months later, we may find that its apparent position has shifted a tiny amount relative to the faraway background stars. By knowing the size of the earth’s orbit and this little angle, we can estimate the distance to the star.
Some stars are close enough to be seen as a disk in high-power telescopes (I believe Betelgeuse is big enough and close enough to see the disk). Most stars appear as points of light in even the largest telescopes, however. To estimate the size of a star where the disk is visible, we simply make a triangle with one angle is the angular radius of the disk, and the side is the distance to the star. The far side is the radius of the star.
Most stars are too far away to use parallax to estimate their distances. Some special kinds of stars, called "Cepheid variable stars", are stars that periodically change their brightness. The time it takes for these stars to dim and get bright again depends on their intrinsic brightness. This is calibrated for nearby Cepheid variable stars and used for faraway ones. By knowing how intrinsically bright a faraway Cepheid variable star is, and by knowing how bright it appears to us, we can estimate how far away it is. If we know other stars are nearby the Cepheid variable, we can use the same distance estimate.''
There is a complete description how a person can measure the distance of a star from earth using a parallax, or if the stars are close enough, using their disk size.
So, Tom, there is no way that the stars can be as close as you said.