{"status": "success", "data": {"description_md": "Let $\\triangle ABC$ be an isosceles triangle with $BC = AC$ and $\\angle ACB = 40^{\\circ}$. Construct the circle with diameter $\\overline{BC}$, and let $D$ and  $E$ be the other intersection points of the circle with the sides $\\overline{AC}$ and $\\overline{AB}$, respectively. Let $F$ be the intersection of the diagonals of the quadrilateral $BCDE$. What is the degree measure of $\\angle BFC ?$\n\n$\\textbf{(A) } 90 \\qquad\\textbf{(B) } 100 \\qquad\\textbf{(C) } 105 \\qquad\\textbf{(D) } 110 \\qquad\\textbf{(E) } 120$", "description_html": "<p>Let  <span class=\"katex--inline\">\\triangle ABC</span>  be an isosceles triangle with  <span class=\"katex--inline\">BC = AC</span>  and  <span class=\"katex--inline\">\\angle ACB = 40^{\\circ}</span> . Construct the circle with diameter  <span class=\"katex--inline\">\\overline{BC}</span> , and let  <span class=\"katex--inline\">D</span>  and   <span class=\"katex--inline\">E</span>  be the other intersection points of the circle with the sides  <span class=\"katex--inline\">\\overline{AC}</span>  and  <span class=\"katex--inline\">\\overline{AB}</span> , respectively. Let  <span class=\"katex--inline\">F</span>  be the intersection of the diagonals of the quadrilateral  <span class=\"katex--inline\">BCDE</span> . What is the degree measure of  <span class=\"katex--inline\">\\angle BFC ?</span> </p>\n<p> <span class=\"katex--inline\">\\textbf{(A) } 90 \\qquad\\textbf{(B) } 100 \\qquad\\textbf{(C) } 105 \\qquad\\textbf{(D) } 110 \\qquad\\textbf{(E) } 120</span> </p>\n<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": "2019 AMC 10A Problem 13", "can_next": true, "can_prev": true, "nxt": "/problem/19_amc10A_p14", "prev": "/problem/19_amc10A_p12"}}