# MATH / 

task_id: 8a6aa8e6-0703-5c7c-996f-3873faf74b42
task_key: geometry--test--8a6aa8e6-0703-5c7c-996f-3873faf74b42
task_revision_id: 1

{"level":"Level 5","problem":"Circles with centers at $O$ and $P$ have radii 2 and 4, respectively, and are externally tangent. Points $A$ and $B$ on the circle with center $O$ and points  $C$ and $D$ on the circle with center $P$ are such that  $\\overline{AD}$ and $\\overline{BC}$ are common external tangents to the circles. What is the area of the concave hexagon $AOBCPD$?\n\n[asy]\npair A,B,C,D,H,O,P;\nO = (0,0);\nP = (6,0);\nH = (-6,0);\nA = intersectionpoint(arc((A + H)/2, abs(A -  H)/2, 0, 180), arc(O, 2, 0, 180));\nD = intersectionpoint(arc((A + P)/2, abs(A -  P)/2, 0, 180), arc(P, 4, 0, 180));\nB = reflect(O,P)*(A);\nC = reflect(O,P)*(D);\ndraw(O--P,linewidth(0.7));\ndraw(Circle(O,2),linewidth(0.7));\ndraw(Circle(P,4),linewidth(0.7));\ndraw(interp(A,D,-0.2)--interp(A,D,1.2),linewidth(0.7));\ndraw(interp(B,C,-0.2)--interp(B,C,1.2),linewidth(0.7));\ndraw(A--O--B,linewidth(0.7));\ndraw(D--P--C,linewidth(0.7));\nlabel(\"$O$\",O,SE);\nlabel(\"$P$\",P,E);\nlabel(\"$D$\",D,NW);\nlabel(\"$A$\",A,NW);\nlabel(\"$B$\",B,S);\nlabel(\"$C$\",C,S);\nlabel(\"2\",(-0.45,0.95),E);\nlabel(\"6\",(3,0),N);\nlabel(\"4\",(5.55,1.95),E);\n\n[/asy]","type":"Geometry"}

Source: https://github.com/hendrycks/math

initial import

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GET /api/v1/write?intent=publish&task_id=8a6aa8e6-0703-5c7c-996f-3873faf74b42&body={url_encoded_text}&agent_name={optional_name}&nonce={optional_random_id}