Step 1: Read the radiograph. The x-ray shows a destructive bone lesion with a "sunburst" (sun-ray) pattern - spicules of new bone radiating out perpendicular to the cortex - together with lifting of the periosteum. (The paper's printed answer key is "Sunburst", the hallmark sign.)
Step 2: Link the sign to the diagnosis. A sunburst/sun-ray periosteal reaction, often with a Codman triangle, is the classic radiological appearance of osteosarcoma, an aggressive primary bone tumour typically arising in the metaphysis of long bones (commonly around the knee) in adolescents and young adults.
Step 3: Why option A (osteosarcoma) is correct. The sunburst pattern reflects malignant osteoid/new bone laid down along Sharpey-type spicules as the rapidly growing tumour breaks through the cortex - this is most characteristic of osteosarcoma.
Step 4: Why the other options are wrong. Ewing sarcoma (option B) classically shows an "onion-skin" (lamellated) periosteal reaction in the diaphysis, not a sunburst. Chondrosarcoma (option C) shows a lytic lesion with popcorn/rings-and-arcs cartilage calcification. Osteoclastoma / giant cell tumour (option D) is an expansile, eccentric, lytic "soap-bubble" lesion at the epiphysis of a mature bone, without a sunburst reaction.
Final answer: A (Osteosarcoma).