центральной

центральной

"Central."

Here, 'центральной' is used as an adjective in the genitive case to describe the square ('площади') of the city ('города') as being central or main.

Я живу недалеко от центральной площади города.

I live near the central square of the city.

In this case, 'центральной' functions as an adjective in the prepositional case to describe the street ('улице') as central or main.

На центральной улице построили новый театр.

A new theater was built on the central street.

Here, 'центральной' appears as an adjective in the genitive case referring to the idea ('идеи') as central or crucial in its importance to the plan.

Это часть центральной идеи его плана.

This is part of the central idea of his plan.