<prompt> Miduara A,B, na C ina mduara wa nje na inasogea ndani ili kuzunguka D. Miduara B na C ni sanjari. Mduara A una radius 1 na hupitia katikati ya D. Mduara wa B ni upi?asyunitsize1cm;jozi A,B,C,D;A-1,0;B0.66,0.88;C0.66,-0.88;D0,0;choraMduaraA,1,upana wa mstari0.7;choraMduaraB,0.88,upana wa mstari0.7;choraMduaraC,0.88,upana wa mstari0.7;choraMduaraD,2,upana wa mstari0.7;leboA,A,A;leboB,B,B;leboC,C,C;leboD,-1.2,1.6,NW;asy  <response>: Acha E,H, na F viwe vitovu vya miduara A,B, na D, mtawalia, na acha G iwe kitovu cha miduara B na C. Hebu xFG na yGH. Kwa kuwa kitovu cha mduara D kiko kwenye mduara A na miduara ina sehemu ya kawaida ya mduara, radius ya duara D ni 2, ambayo ni kipenyo cha mduara A. Kutumia Nadharia ya Pythagorean kwa pembetatu za kulia EGH na FGH inatoa 1y2 1x2 y2 quadtextnaquad 2-y2 x2 y2, ambayo inafuata kwamba y x fracx22 quadtextnaquad y 1 - fracx24. Masuluhisho ya mfumo huu ni x,y23, 89 na x,y-2, 0. Radi ya mduara B ndio suluhu chanya kwa y, ambayo ni frac89.asyunitsize2.2cm;jozi A,B,C,D;A-1,0;B0.66,0.88;C0.66,-0.88;D0,0;choraMduaraA,1,upana wa mstari0.7;choraMduaraB,0.88,upana wa mstari0.7;choraMduaraC,0.88,upana wa mstari0.7;choraMduaraD,2,upana wa mstari0.7;leboE,A,W;leboH,B,N;leboy,1,1.2,S;leboy,0.66,0.44,E;leboG,0.66,0,S;leboy,0.2,0.6,N;lebox,0.45,-0.1,S;chora0,0--1.2,1.6,upana wa mstari0.7;lebomizani0.7zungusha552-y,0.33,0.44,E;lebo1,-0.8,0.2,N;lebo1,-0.7,0,S;chora-1,0--0.66,0.88--0.66,0--mzunguko,upana wa mstari0.7;asy 