{"status": "success", "data": {"description_md": "Triangle $ABC$ has side lengths in arithmetic progression, and the smallest side has length $6$. If the triangle has an angle of $120^\\circ,$ what is the area of $ABC$?\n\n$\\textbf{(A) }12\\sqrt{3}\\qquad\\textbf{(B) }8\\sqrt{6}\\qquad\\textbf{(C) }14\\sqrt{2}\\qquad\\textbf{(D) }20\\sqrt{2}\\qquad\\textbf{(E) }15\\sqrt{3}$\n___\nFull credit goes to [MAA](https://maa.org/) for authoring these problems. These problems were taken on the [AOPS](https://artofproblemsolving.com/) website.", "description_html": "<p>Triangle  <span class=\"katex--inline\">ABC</span>  has side lengths in arithmetic progression, and the smallest side has length  <span class=\"katex--inline\">6</span> . If the triangle has an angle of  <span class=\"katex--inline\">120^\\circ,</span>  what is the area of  <span class=\"katex--inline\">ABC</span> ?</p>&#10;<p> <span class=\"katex--inline\">\\textbf{(A) }12\\sqrt{3}\\qquad\\textbf{(B) }8\\sqrt{6}\\qquad\\textbf{(C) }14\\sqrt{2}\\qquad\\textbf{(D) }20\\sqrt{2}\\qquad\\textbf{(E) }15\\sqrt{3}</span> </p>&#10;<hr><p>Full credit goes to <a href=\"https://maa.org/\">MAA</a> for authoring these problems. These problems were taken on the <a href=\"https://artofproblemsolving.com/\">AOPS</a> website.</p>", "hints_md": "", "hints_html": "", "editorial_md": "", "editorial_html": "", "flag_hint": "", "point_value": 3, "problem_name": "2023 AMC 12B Problem 17", "can_next": true, "can_prev": true, "nxt": "/problem/23_amc12B_p18", "prev": "/problem/23_amc12B_p16"}}