{"status": "success", "data": {"description_md": "A segment through the focus $F$ of a parabola with vertex $V$ is perpendicular to $\\overline{FV}$ and intersects the parabola in points $A$ and $B$. What is $\\cos\\left(\\angle AVB\\right)$?\n\n$\\textbf{(A)}\\ -\\frac{3\\sqrt{5}}{7} \\qquad \\textbf{(B)}\\ -\\frac{2\\sqrt{5}}{5} \\qquad \\textbf{(C)}\\ -\\frac{4}{5} \\qquad \\textbf{(D)}\\ -\\frac{3}{5} \\qquad \\textbf{(E)}\\ -\\frac{1}{2}$\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>A segment through the focus  <span class=\"katex--inline\">F</span>  of a parabola with vertex  <span class=\"katex--inline\">V</span>  is perpendicular to  <span class=\"katex--inline\">\\overline{FV}</span>  and intersects the parabola in points  <span class=\"katex--inline\">A</span>  and  <span class=\"katex--inline\">B</span> . What is  <span class=\"katex--inline\">\\cos\\left(\\angle AVB\\right)</span> ?</p>&#10;<p> <span class=\"katex--inline\">\\textbf{(A)}\\ -\\frac{3\\sqrt{5}}{7} \\qquad \\textbf{(B)}\\ -\\frac{2\\sqrt{5}}{5} \\qquad \\textbf{(C)}\\ -\\frac{4}{5} \\qquad \\textbf{(D)}\\ -\\frac{3}{5} \\qquad \\textbf{(E)}\\ -\\frac{1}{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": "2011 AMC 12B Problem 14", "can_next": true, "can_prev": true, "nxt": "/problem/11_amc12B_p15", "prev": "/problem/11_amc12B_p13"}}