How Do Astronomers Know That Pulsating Variable Stars Are Actually

Multiple Choice

How do astronomers know that pulsating variable stars are actually expanding and contracting in diameter?

A) it is clear just by looking at the light curve
B) they discover this by looking at an H-R diagram
C) they can measure a regularly varying Doppler shift in the spectral lines
D) they can measure the star's changing pull on a companion star around it
E) astronomers are just guessing; at the distances of the stars, there is no way to show that stars are expanding and contracting