<prompt> Kipenyo cha AB cha mduara wa radius 2 kinapanuliwa hadi hatua D nje ya mduara ili BD3. Pointi E imechaguliwa ili ED5 na mstari ED iwe sawa na mstari AD. Sehemu ya AE inakatiza mduara kwa uhakika C kati ya A na E. Je! eneo la pembetatu ABC ni nini?textbfA frac12037qquadtextbfB frac14039qquadtextbfC frac145 39qquadtextbfD frac14037qquadtextbfE frac12031  <response>: asy Geogebra hadi Asymptote ubadilishaji, hati katika artofproblemsolving.comWiki, nenda kwa User:Azjpsgeogebra import grafu; ukubwa 8.865514650638614cm; labelscalefactor halisi 0.5; hubadilisha umbali wa lebo-kwa-point kalamu dps upana wa mstari0.7 fontsize10; defaultpendps; mtindo wa kalamu chaguo-msingi kalamu dotstyle nyeusi; mtindo wa uhakika xmin halisi -6.36927122464312, xmax 11.361758076634109, ymin -3.789601803155515, ymax 7.42001502629601 vipimo vya picha chora-2.,0.--0.6486486486486486,1.8918918918918919--2.,0.--mzunguko; chora takwimu choramduara0.,0., 2.; chora-2.,0.--5.,5.; chora5.,5.--5.,0.; chora5.,0.---2.,0.; kuchora-2.,0.--0.6486486486486486,1.8918918918918919; kuchora0.6486486486486486,1.8918918918918919--2.,0.; chora2.,0.---2.,0.; chora2.,0.--5.,5.; chora0.,0.--5.,5.; nukta na lebo nukta0.,0.,dotstyle; leboO, -0.10330578512396349,-0.39365890308038826, NE labelscalefactor; nukta -2.,0., mtindo wa nukta; leboA, -2.2370398196844437,-0.42371149511645134, NE labelscalefactor; nukta 2.,0., mtindo wa nukta; leboB, 2.045454545454548,-0.36360631104432517, NE labelscalefactor; nukta 5.,0., mtindo wa nukta; leboD, 4.900450788880542,-0.42371149511645134, NE labelscalefactor; nukta 5.,5., mtindo wa nukta; leboE, 5.06574004507889,5.15104432757325, NE labelscalefactor; nukta0.6486486486486486,1.8918918918918919,linewidth3.pt dotstyle; leboC, 0.48271975957926694,2.100706235912847, NE labelscalefactor; klipuxmin,ymin--xmin,ymax--xmax,ymax--xmax,ymin--mzunguko; mwisho wa picha asyAcha O iwe kitovu cha mduara. Kumbuka kuwa EC CA EA sqrtAD2 DE2 sqrt2232 52 sqrt74. Hata hivyo, kwa Nguvu ya Pointi, ECEC CA EO2 - R2 232 52 - 22 25 25 - 4 46 inamaanisha EC frac46sqrt74, hivyo AC sqrt74 - frac46sqrt74 frac28sqrt74 . Sasa BC sqrtAB2 - AC2 sqrt42 - frac28274 sqrtfrac16 cdot 74 - 282 74 sqrtfrac1184 - 78474 frac20sqrt74. Kwa kuwa angle ACB 90circ, ABC frac12 cdot BC cdot AC frac12 cdot frac20sqrt 74 cdot frac28sqrt74 frac14037. 