Final answer:
Centrioles are the organelles near the nucleus that organize microtubules to form spindle fibers during cell division, ensuring correct chromosome segregation to daughter cells.
Step-by-step explanation:
The cell organelles that are visible during cell division and act as sites where the spindle fibers originate are known as centrioles. Centrioles are found only in animal cells and are positioned near the nucleus serving a crucial role in cellular division. They are comprised of a cylindrical arrangement of microtubules, typically forming a structure with nine groups of three microtubules each. Two centrioles lie perpendicular to each other, making up the centrosome, which is the microtubule-organizing center in the cell. During mitosis, centrioles help to arrange the mitotic spindles that are responsible for pulling the chromosomes apart. It is essential for ensuring that each daughter cell ends up with the correct number of chromosomes.