{"status": "success", "data": {"description_md": "Let $A = (0,9)$ and $B = (0,12)$. Points $A'$ and $B'$ are on the line $y = x$, and $\\overline{AA'}$ and $\\overline{BB'}$ intersect at $C = (2,8)$. What is the length of $\\overline{A'B'}$?\n\n$\\text {(A) } 2 \\qquad \\text {(B) } 2\\sqrt2 \\qquad \\text {(C) } 3 \\qquad \\text {(D) } 2 + \\sqrt 2\\qquad \\text {(E) }3\\sqrt 2$\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>Let  <span class=\"katex--inline\">A = (0,9)</span>  and  <span class=\"katex--inline\">B = (0,12)</span> . Points  <span class=\"katex--inline\">A'</span>  and  <span class=\"katex--inline\">B'</span>  are on the line  <span class=\"katex--inline\">y = x</span> , and  <span class=\"katex--inline\">\\overline{AA'}</span>  and  <span class=\"katex--inline\">\\overline{BB'}</span>  intersect at  <span class=\"katex--inline\">C = (2,8)</span> . What is the length of  <span class=\"katex--inline\">\\overline{A'B'}</span> ?</p>&#10;<p> <span class=\"katex--inline\">\\text {(A) } 2 \\qquad \\text {(B) } 2\\sqrt2 \\qquad \\text {(C) } 3 \\qquad \\text {(D) } 2 + \\sqrt 2\\qquad \\text {(E) }3\\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": 3, "problem_name": "2004 AMC 12A Problem 12", "can_next": true, "can_prev": true, "nxt": "/problem/04_amc12A_p13", "prev": "/problem/04_amc12A_p11"}}