Why was the geocentric model of the solar system accepted by scientist for many years?

Because of the its assumption of earth being at the centre of the universe and also, its parallax argument.

Explanation: Geocentric model is the

theory of the structure of the solar system (or the universe) in which Earth  is assumed to be at the centre of it all. It was generally accepted until the 16th century, after which it was superseded by heliocentric models 

Among many, geocentric model was considered because of its stellar parallax argument.

What is parallax? Parallax is the apparent change in position of objects due to a change in observation location

The ancient Greeks claimed that if the Earth is moving around the Sun then the stars should shift their positions due to this orbital motion (called stellar parallax). The stars don't shift. They don't shift enough for you to notice, but they do indeed shift. This is essentially the same reason the moon appears to follow you around when you drive - it's too far away for any apparent shift due to your motion.

half of a circle

explanation:

the arrow and the top of the circle is matching together. it is not a polygon because a polygon would always be the same shape. therefore, an half of a circle is called semicircle so you would find the radius of it.