{"status": "success", "data": {"description_md": "In $\\triangle ABC$, $AB=13$, $AC=5$, and $BC=12$. Points $M$ and $N$ lie on $AC$ and $BC$, respectively, with $CM=CN=4$. Points $J$ and $K$ are on $AB$ so that $MJ$ and $NK$ are perpendicular to $AB$. What is the area of pentagon $CMJKN$?
[asy] unitsize(0.5cm); defaultpen(0.8); pair C=(0,0), A=(0,5), B=(12,0), M=(0,4), N=(4,0); pair J=intersectionpoint(A--B, M--(M+rotate(90)*(B-A)) ); pair K=intersectionpoint(A--B, N--(N+rotate(90)*(B-A)) ); draw( A--B--C--cycle ); draw( M--J ); draw( N--K ); label(\"$A$\",A,NW); label(\"$B$\",B,SE); label(\"$C$\",C,SW); label(\"$M$\",M,SW); label(\"$N$\",N,S); label(\"$J$\",J,NE); label(\"$K$\",K,NE); [/asy]
\n\n$\\mathrm{(A)}\\ 15 \\qquad \\mathrm{(B)}\\ \\frac{81}{5}\\qquad\\mathrm{(C)}\\ \\frac{205}{12}\\qquad\\mathrm{(D)}\\ \\frac{240}{13}\\qquad\\mathrm{(E)}\\ 20$\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": "

In \\triangle ABC , AB=13 , AC=5 , and BC=12 . Points M and N lie on AC and BC , respectively, with CM=CN=4 . Points J and K are on AB so that MJ and NK are perpendicular to AB . What is the area of pentagon CMJKN ?

\"[asy]

\\mathrm{(A)}\\ 15 \\qquad \\mathrm{(B)}\\ \\frac{81}{5}\\qquad\\mathrm{(C)}\\ \\frac{205}{12}\\qquad\\mathrm{(D)}\\ \\frac{240}{13}\\qquad\\mathrm{(E)}\\ 20

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.

", "hints_md": "", "hints_html": "", "editorial_md": "", "editorial_html": "", "flag_hint": "", "point_value": 3, "problem_name": "2004 AMC 12B Problem 14", "can_next": true, "can_prev": true, "nxt": "/problem/04_amc12B_p15", "prev": "/problem/04_amc12B_p13"}}