{"status": "success", "data": {"description_md": "Circles with centers $P, Q$ and $R$, having radii $1, 2$ and $3$, respectively, lie on the same side of line $l$ and are tangent to $l$ at $P', Q'$ and $R'$, respectively, with $Q'$ between $P'$ and $R'$. The circle with center $Q$ is externally tangent to each of the other two circles. What is the area of triangle $PQR$?\n\n$\\textbf{(A) } 0\\qquad \\textbf{(B) } \\frac{\\sqrt{6}}{3}\\qquad\\textbf{(C) } 1\\qquad\\textbf{(D) } \\sqrt{6}-\\sqrt{2}\\qquad\\textbf{(E) }\\frac{\\sqrt{6}}{2}$\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>Circles with centers  <span class=\"katex--inline\">P, Q</span>  and  <span class=\"katex--inline\">R</span> , having radii  <span class=\"katex--inline\">1, 2</span>  and  <span class=\"katex--inline\">3</span> , respectively, lie on the same side of line  <span class=\"katex--inline\">l</span>  and are tangent to  <span class=\"katex--inline\">l</span>  at  <span class=\"katex--inline\">P', Q'</span>  and  <span class=\"katex--inline\">R'</span> , respectively, with  <span class=\"katex--inline\">Q'</span>  between  <span class=\"katex--inline\">P'</span>  and  <span class=\"katex--inline\">R'</span> . The circle with center  <span class=\"katex--inline\">Q</span>  is externally tangent to each of the other two circles. What is the area of triangle  <span class=\"katex--inline\">PQR</span> ?</p>&#10;<p> <span class=\"katex--inline\">\\textbf{(A) } 0\\qquad \\textbf{(B) } \\frac{\\sqrt{6}}{3}\\qquad\\textbf{(C) } 1\\qquad\\textbf{(D) } \\sqrt{6}-\\sqrt{2}\\qquad\\textbf{(E) }\\frac{\\sqrt{6}}{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": 3, "problem_name": "2016 AMC 12A Problem 15", "can_next": true, "can_prev": true, "nxt": "/problem/16_amc12A_p16", "prev": "/problem/16_amc12A_p14"}}