{"status": "success", "data": {"description_md": "In the figure, $\\angle EAB$ and $\\angle ABC$ are right angles. $AB=4, BC=6, AE=8$, and $AC$ and $BE$ intersect at $D$. What is the difference between the areas of $\\triangle ADE$ and $\\triangle BDC$?\n\n<center>\n<img class=\"problem-image\" height=\"252\" src=\"https://latex.artofproblemsolving.com/3/7/d/37d48968371e6d998d5b4c40c47c99005f414ab9.png\" width=\"152\"/>\n</center>\n\n$\\mathrm{(A) \\ } 2 \\qquad \\mathrm{(B) \\ } 4 \\qquad \\mathrm{(C) \\ } 5 \\qquad \\mathrm{(D) \\ } 8 \\qquad \\mathrm{(E) \\ } 9$", "description_html": "<p>In the figure,  <span class=\"katex--inline\">\\angle EAB</span>  and  <span class=\"katex--inline\">\\angle ABC</span>  are right angles.  <span class=\"katex--inline\">AB=4, BC=6, AE=8</span> , and  <span class=\"katex--inline\">AC</span>  and  <span class=\"katex--inline\">BE</span>  intersect at  <span class=\"katex--inline\">D</span> . What is the difference between the areas of  <span class=\"katex--inline\">\\triangle ADE</span>  and  <span class=\"katex--inline\">\\triangle BDC</span> ?</p>\n<center>\n<img class=\"problem-image\" height=\"252\" src=\"https://latex.artofproblemsolving.com/3/7/d/37d48968371e6d998d5b4c40c47c99005f414ab9.png\" width=\"152\"/>\n</center>\n<p> <span class=\"katex--inline\">\\mathrm{(A) \\ } 2 \\qquad \\mathrm{(B) \\ } 4 \\qquad \\mathrm{(C) \\ } 5 \\qquad \\mathrm{(D) \\ } 8 \\qquad \\mathrm{(E) \\ } 9</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": 1, "problem_name": "2004 AMC 10A Problem 9", "can_next": true, "can_prev": true, "nxt": "/problem/04_amc10A_p10", "prev": "/problem/04_amc10A_p08"}}