{"status": "success", "data": {"description_md": "Suppose that on a parabola with vertex $V$ and a focus $F$ there exists a point $A$ such that $AF=20$ and $AV=21$. What is the sum of all possible values of the length $FV?$\n\n$\\textbf{(A) }13 \\qquad \\textbf{(B) }\\frac{40}3 \\qquad \\textbf{(C) }\\frac{41}3 \\qquad \\textbf{(D) }14\\qquad \\textbf{(E) }\\frac{43}3$\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>Suppose that on a parabola with vertex  <span class=\"katex--inline\">V</span>  and a focus  <span class=\"katex--inline\">F</span>  there exists a point  <span class=\"katex--inline\">A</span>  such that  <span class=\"katex--inline\">AF=20</span>  and  <span class=\"katex--inline\">AV=21</span> . What is the sum of all possible values of the length  <span class=\"katex--inline\">FV?</span> </p>&#10;<p> <span class=\"katex--inline\">\\textbf{(A) }13 \\qquad \\textbf{(B) }\\frac{40}3 \\qquad \\textbf{(C) }\\frac{41}3 \\qquad \\textbf{(D) }14\\qquad \\textbf{(E) }\\frac{43}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": "2021 AMC 12A Problem 20", "can_next": true, "can_prev": true, "nxt": "/problem/21_amc12A_p21", "prev": "/problem/21_amc12A_p19"}}