Antioxidants and Free Radicals and vascular growth factors.
The tumor grows fast, and outgrows its blood supply. That means that some of the tumor cells are hypoxic [alive, but not getting enough oxygen from the blood supply]. Hypoxic tumor cells make free radicals [sometimes called reactive oxygen species], which then cause the tumor cells to make vascular growth factors. These are small molecules like EGF, VEGF, PDGF; that, then are released to attract endothelial cells. These cells line the blood vessels, and which start the framework for new blood vessel growth. So tumor hypoxia leads to free radicals, which lead to vascular growth factors, which lead to angiogenesis [growth of new blood vessels].
Antioxidants like Vitamin C, Vitamin E, NAC, acetyl l-carnitine, alpha lipoic acid, etc. react with free radicals and render them useless. So taking antioxidants can prevent angiogenesis.