{"status": "success", "data": {"description_md": "Distinct points $A$, $B$, $C$, and $D$ lie on a line, with $AB=BC=CD=1$. Points $E$ and $F$ lie on a second line, parallel to the first, with $EF=1$. A triangle with positive area has three of the six points as its vertices. How many possible values are there for the area of the triangle?\n\n$\\text{(A) } 3\n\\qquad\n\\text{(B) } 4\n\\qquad\n\\text{(C) } 5\n\\qquad\n\\text{(D) } 6\n\\qquad\n\\text{(E) } 7$", "description_html": "<p>Distinct points  <span class=\"katex--inline\">A</span> ,  <span class=\"katex--inline\">B</span> ,  <span class=\"katex--inline\">C</span> , and  <span class=\"katex--inline\">D</span>  lie on a line, with  <span class=\"katex--inline\">AB=BC=CD=1</span> . Points  <span class=\"katex--inline\">E</span>  and  <span class=\"katex--inline\">F</span>  lie on a second line, parallel to the first, with  <span class=\"katex--inline\">EF=1</span> . A triangle with positive area has three of the six points as its vertices. How many possible values are there for the area of the triangle?</p>\n<p> <span class=\"katex--inline\">\\text{(A) } 3\n\\qquad\n\\text{(B) } 4\n\\qquad\n\\text{(C) } 5\n\\qquad\n\\text{(D) } 6\n\\qquad\n\\text{(E) } 7</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": "2009 AMC 10B Problem 12", "can_next": true, "can_prev": true, "nxt": "/problem/09_amc10B_p13", "prev": "/problem/09_amc10B_p11"}}