Final answer:
External beam radiation therapy is the best type of radiation therapy to treat a bronchogenic carcinoma that has extended into the mediastinum and around the superior vena cava.
Step-by-step explanation:
The best type of radiation therapy to treat a bronchogenic carcinoma that has grown into the mediastinum and around the superior vena cava is external beam radiation therapy. This technique involves directing multiple beams of high-energy radiation, such as X-rays, from different angles towards the cancerous tissue. The rays intersect at the site of the cancer, delivering a larger dose of radiation to the tumor while limiting the exposure of surrounding healthy tissue.