Which of the following conditions increases the risk of osteosarcoma?

Paget's disease is known to increase the risk of osteosarcoma, particularly because the rapid bone remodeling and alterations in the normal structure of bone associated with Paget's can lead to malignant transformation. In Paget's disease, the bone undergoes abnormal growth, which can create an environment that is more conducive to the development of certain types of bone tumors, including osteosarcoma.

In contrast, while conditions like rickets, arthritis, and osteoporosis involve bone health, they are not typically associated with an elevated risk of developing osteosarcoma. Rickets primarily affects bone mineralization due to vitamin D deficiency, arthritis leads to inflammation and joint damage without an increased risk for bone tumors, and osteoporosis results in decreased bone density but does not inherently promote the development of osteosarcoma. Thus, Paget's disease stands out as a significant risk factor for this type of bone cancer.