{"status": "success", "data": {"description_md": "Suppose that $\\triangle ABC$ is an equilateral triangle of side length $s$, with the property that there is a unique point $P$ inside the triangle such that $AP = 1$, $BP = \\sqrt{3}$, and $CP = 2$. What is $s?$\n\n$\\textbf{(A) } 1 + \\sqrt{2} \\qquad \\textbf{(B) } \\sqrt{7} \\qquad \\textbf{(C) } \\frac{8}{3} \\qquad \\textbf{(D) } \\sqrt{5 + \\sqrt{5}} \\qquad \\textbf{(E) } 2\\sqrt{2}$\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>Suppose that  <span class=\"katex--inline\">\\triangle ABC</span>  is an equilateral triangle of side length  <span class=\"katex--inline\">s</span> , with the property that there is a unique point  <span class=\"katex--inline\">P</span>  inside the triangle such that  <span class=\"katex--inline\">AP = 1</span> ,  <span class=\"katex--inline\">BP = \\sqrt{3}</span> , and  <span class=\"katex--inline\">CP = 2</span> . What is  <span class=\"katex--inline\">s?</span> </p>&#10;<p> <span class=\"katex--inline\">\\textbf{(A) } 1 + \\sqrt{2} \\qquad \\textbf{(B) } \\sqrt{7} \\qquad \\textbf{(C) } \\frac{8}{3} \\qquad \\textbf{(D) } \\sqrt{5 + \\sqrt{5}} \\qquad \\textbf{(E) } 2\\sqrt{2}</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": 5, "problem_name": "2020 AMC 12A Problem 24", "can_next": true, "can_prev": true, "nxt": "/problem/20_amc12A_p25", "prev": "/problem/20_amc12A_p23"}}