{"status": "success", "data": {"description_md": "<!--[[Image:2006_AMC10A-16.png]]-->\n\n<center>\n<img class=\"problem-image\" height=\"335\" src=\"https://latex.artofproblemsolving.com/f/4/a/f4a115a9c8dc91a741d0149edb037b3cb07f6b01.png\" width=\"252\"/>\n</center>\nA circle of radius 1 is tangent to a circle of radius 2. The sides of $\\triangle ABC$ are tangent to the circles as shown, and the sides $\\overline{AB}$  and $\\overline{AC}$  are congruent. What is the area of $\\triangle ABC$?\n\n$\\mathrm{(A)}\\ \\frac{35}{2}\\qquad\\mathrm{(B)}\\ 15\\sqrt{2}\\qquad\\mathrm{(C)}\\ \\frac{64}{3}\\qquad\\mathrm{(D)}\\ 16\\sqrt{2}\\qquad\\mathrm{(E)}\\ 24$", "description_html": "<!--[[Image:2006_AMC10A-16.png]]-->\n<center>\n<img class=\"problem-image\" height=\"335\" src=\"https://latex.artofproblemsolving.com/f/4/a/f4a115a9c8dc91a741d0149edb037b3cb07f6b01.png\" width=\"252\"/>\n</center>\nA circle of radius 1 is tangent to a circle of radius 2. The sides of $\\triangle ABC$ are tangent to the circles as shown, and the sides $\\overline{AB}$  and $\\overline{AC}$  are congruent. What is the area of $\\triangle ABC$?\n<p> <span class=\"katex--inline\">\\mathrm{(A)}\\ \\frac{35}{2}\\qquad\\mathrm{(B)}\\ 15\\sqrt{2}\\qquad\\mathrm{(C)}\\ \\frac{64}{3}\\qquad\\mathrm{(D)}\\ 16\\sqrt{2}\\qquad\\mathrm{(E)}\\ 24</span> </p>\n<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": "2006 AMC 10A Problem 16", "can_next": true, "can_prev": true, "nxt": "/problem/06_amc10A_p17", "prev": "/problem/06_amc10A_p15"}}