{"status": "success", "data": {"description_md": "Let $\\overline{AB}$ be a diameter in a circle of radius $5\\sqrt2.$ Let $\\overline{CD}$ be a chord in the circle that intersects $\\overline{AB}$ at a point $E$ such that $BE=2\\sqrt5$ and $\\angle AEC = 45^{\\circ}.$ What is $CE^2+DE^2?$\n\n$\\textbf{(A)}\\ 96 \\qquad\\textbf{(B)}\\ 98 \\qquad\\textbf{(C)}\\  44\\sqrt5 \\qquad\\textbf{(D)}\\ 70\\sqrt2 \\qquad\\textbf{(E)}\\ 100$\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\">\\overline{AB}</span>  be a diameter in a circle of radius  <span class=\"katex--inline\">5\\sqrt2.</span>  Let  <span class=\"katex--inline\">\\overline{CD}</span>  be a chord in the circle that intersects  <span class=\"katex--inline\">\\overline{AB}</span>  at a point  <span class=\"katex--inline\">E</span>  such that  <span class=\"katex--inline\">BE=2\\sqrt5</span>  and  <span class=\"katex--inline\">\\angle AEC = 45^{\\circ}.</span>  What is  <span class=\"katex--inline\">CE^2+DE^2?</span> </p>&#10;<p> <span class=\"katex--inline\">\\textbf{(A)}\\ 96 \\qquad\\textbf{(B)}\\ 98 \\qquad\\textbf{(C)}\\  44\\sqrt5 \\qquad\\textbf{(D)}\\ 70\\sqrt2 \\qquad\\textbf{(E)}\\ 100</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": "2020 AMC 12B Problem 12", "can_next": true, "can_prev": true, "nxt": "/problem/20_amc12B_p13", "prev": "/problem/20_amc12B_p11"}}