<prompt> Acha G na H zionyeshe katikati na katikati ya pembetatu ABC, mtawalia. Acha F iwe kitovu cha overlineGH. Express AF2 BF2 CF2 kulingana na urefu wa upande a, b, c na circumradius R ya pembetatu ABC.  <response>: Ruhusu kipenyo cha O cha pembetatu ABC kiwe asili. KishaoverrightarrowG fracoverrightarrowA overrightarrowB overrightarrowC3na overrightarrowH overrightarrowA overrightarrow B mshale wa kuliaC, hivyooverrightarrowF frac23 overrightarrowA overrightarrowB overrightarrowC.KishaanzaalignAF2 mshale wa kulia zaidiA - ushale wa kuliaF2 kushoto mshale wa kulia zaidiA - frac23 mshale wa kulia zaidiA ushale uliopitilizaB ushale uliopitilizaC kulia2 kushoto frac13 overrightarrowA - frac23 overrightarrowB - frac23 overrightarrowC right2 frac19 arrow kuliaA - 2 arrowoverrightarrowB - 2 overrightarrowC2 frac19 arrow overrightarrowA - 2 overrightarrowB - 2 overrightarrowC cdot overrightarrowA - 2 overrightarrowB - 2 overrightarrow C frac19 overrightarrowA cdot overrightarrowA 4 overrightarrowB cdot overrightarrowB 4 overrightarrowC cdot overrightarrowC - 4 mshale ulio kulia zaidiA cdot mshale ulio kulia zaidiB - 4 mshale ulio kulia zaidiA cdot ushale ulio juu zaidiC 8 ushale uliopitilizaB cdot ushale uliopitilizaC frac19 9R2 - 4 arrowoverrightarrowA cdot overrightarrowB - 4 overrightarrowA cdot overrightarrowC 8 overrightarrowB cdot mshale wa kulia zaidiC.mwishoalignVile vile,anzaalignBF2 frac19 9R2 - 4 arrow overrightarrowA cdot overrightarrowB 8 overrightarrowA cdot overrightarrowC - 4 overrightarrow B cdoti mshale wa kuliaC, CF2 frac19 9R2 8 arrowoverrightarrowA cdot overrightarrowB - 4 overrightarrowA cdot overrightarrowC - 4 overrightarrow B cdot mshale wa kuliaC.mwishoalignHivyo, AF2 BF2 CF2 3R2. 