¥begin{tikzpicture}[scale=1.5]
¥tikzmath{
	¥b = 3; %CDの長さ
	¥c = sqrt(11); %DBの長さ
	¥d = 1; %BCの長さ
	¥B = acos((¥c^2+¥d^2-¥b^2)/(2*¥c*¥d));
	¥C = acos((¥d^2+¥b^2-¥c^2)/(2*¥d*¥b));
	¥D = acos((¥b^2+¥c^2-¥d^2)/(2*¥b*¥c));
	¥R = ¥b/(2*sin(¥B));
}
¥coordinate (C) at (0,0);
¥coordinate (B) at (¥C:¥d);
¥coordinate (D) at (0:¥b);
%¥coordinate[label=above:O] (O) at (90-¥B:¥R);
¥coordinate (O) at (90-¥B:¥R);
¥draw[name path=C1] (O) circle[radius=¥R];
¥path[name path=C2] (B) circle[radius=2];
¥path[name intersections={of=C1 and C2, by={A}}];%C1とC2の2交点の内の1つをAとする
¥coordinate (A) at (intersection-1) node [above] at (A) {A};
¥draw[thick] (A)--(B)--(C)--(D)--cycle;
¥draw[dashed,very thin]
(C) to[bend right=20] node[fill=white,midway]{$¥b$} (D)
(B) to[bend right=50] node[fill=white,midway]{$¥d$} (C)
(A) to[bend right=20] node[fill=white,midway]{$2$} (B);
%¥fill (O) circle[radius=1pt];
¥foreach ¥P in{B,C,D} ¥draw ($(O)!11/10!(¥P)$) node{¥P};
¥end{tikzpicture}

[与えられた条件]
円に内接する四角形ABCDにおいて，$${\text{AB}=2，\text{BC}=1，\text{CD}=3，\cos ∠\text{BCD}=-\dfrac{1}{6}}$$とする。