{"status": "success", "data": {"description_md": "In the overlapping triangles $\\triangle{ABC}$ and $\\triangle{ABE}$ sharing common side $AB$, $\\angle{EAB}$ and $\\angle{ABC}$ are right angles, $AB=4$, $BC=6$, $AE=8$, and $\\overline{AC}$ and $\\overline{BE}$ intersect at $D$. What is the difference between the areas of $\\triangle{ADE}$ and $\\triangle{BDC}$? \n\n$\\text{(A) } 2 \\qquad \\text{(B) } 4 \\qquad \\text{(C) } 5 \\qquad \\text{(D) } 8 \\qquad \\text{(E) } 9 \\qquad$<br><center><img class=\"problem-image\" alt='[asy] size(150); defaultpen(linewidth(0.4)); //Variable Declarations pair A, B, C, D, E;  //Variable Definitions A=(0, 0); B=(4, 0); C=(4, 6); E=(0, 8); D=extension(A,C,B,E);  //Initial Diagram draw(A--B--C--A--E--B); label(\"$A$\",A,SW); label(\"$B$\",B,SE); label(\"$C$\",C,NE); label(\"$D$\",D,3N); label(\"$E$\",E,NW);  //Side labels label(\"$4$\",A--B,S); label(\"$8$\",A--E,W); label(\"$6$\",B--C,ENE); [/asy]' class=\"latexcenter\" height=\"252\" src=\"https://latex.artofproblemsolving.com/3/7/d/37d48968371e6d998d5b4c40c47c99005f414ab9.png\" width=\"152\"/></center>\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>In the overlapping triangles  <span class=\"katex--inline\">\\triangle{ABC}</span>  and  <span class=\"katex--inline\">\\triangle{ABE}</span>  sharing common side  <span class=\"katex--inline\">AB</span> ,  <span class=\"katex--inline\">\\angle{EAB}</span>  and  <span class=\"katex--inline\">\\angle{ABC}</span>  are right angles,  <span class=\"katex--inline\">AB=4</span> ,  <span class=\"katex--inline\">BC=6</span> ,  <span class=\"katex--inline\">AE=8</span> , and  <span class=\"katex--inline\">\\overline{AC}</span>  and  <span class=\"katex--inline\">\\overline{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>&#10;<p> <span class=\"katex--inline\">\\text{(A) } 2 \\qquad \\text{(B) } 4 \\qquad \\text{(C) } 5 \\qquad \\text{(D) } 8 \\qquad \\text{(E) } 9 \\qquad</span> <br/><center><img class=\"latexcenter\" alt=\"[asy] size(150); defaultpen(linewidth(0.4)); //Variable Declarations pair A, B, C, D, E;  //Variable Definitions A=(0, 0); B=(4, 0); C=(4, 6); E=(0, 8); D=extension(A,C,B,E);  //Initial Diagram draw(A--B--C--A--E--B); label(&#34;$A$&#34;,A,SW); label(&#34;$B$&#34;,B,SE); label(&#34;$C$&#34;,C,NE); label(&#34;$D$&#34;,D,3N); label(&#34;$E$&#34;,E,NW);  //Side labels label(&#34;$4$&#34;,A--B,S); label(&#34;$8$&#34;,A--E,W); label(&#34;$6$&#34;,B--C,ENE); [/asy]\" height=\"252\" src=\"https://latex.artofproblemsolving.com/3/7/d/37d48968371e6d998d5b4c40c47c99005f414ab9.png\" width=\"152\"/></center></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": 2, "problem_name": "2004 AMC 12A Problem 8", "can_next": true, "can_prev": true, "nxt": "/problem/04_amc12A_p09", "prev": "/problem/04_amc12A_p07"}}