The star's collapsed core is not a normal star. It is a neutron star or a black hole:

It is difficult to draw on the same sheet of paper the relative sizes of black holes, neutron stars, white dwarfs, the Sun, and red supergiants. Their size differences are so vast.

If you represent the diameter of a three-solar-mass-black hole (namely, its event horizon) by a dot 1/64 of an inch across, the size of a 1.4-solar-mass neutron star would be only slightly larger. But the size of a white dwarf would be about one foot, that of the Sun would be 38 yards, and that of a red supergiant, such as Betelgeuse, would be 22 miles.

The true sizes of these objects range from 10 miles for a three solar mass black hole to 875,000,000 miles for Betelgeuse.