<prompt> Katika pembetatu ABC, AB 3 na AC 5. Acha O iwe kiduara cha pembetatu ABC. Tafuta overrightarrowOA cdot overrightarrowBC.  <response>: Hebu mathbfa overrightarrowOA, mathbfb overrightarrowOB, na mathbfc overrightarrowOC. KishaoverrightarrowAB overrightarrowOB - overrightarrowOA mathbfb - mathbfa.Vile vile, overrightarrowAC mathbfc - mathbfa na overrightarrowBC mathbfc - mathbfb. Kisha tunataka kukokotoa overrightarrowOA cdot overrightarrowBC mathbfa cdot mathbfc - mathbfb mathbfa cdot mathbfc - mathbfa cdot mathbfb.asyukubwa wa kitengo 2 cm;jozi A, B, C, O;A dir100;B dir200;C dir340;O 0,0;choraMduaraO,1;kuchoraA--B--C--mzunguko;choraO--A,Arrow6;choraO--B,Arrow6;choraO--C,Arrow6;leboA, A, A;leboB, B, B;leboC, C, C;leboO, O, NE;lebomathbfa, A2, SW;lebomathbfb, B2, SE;lebomathbfc, C2, SW;asyKwa kuwa AC 5, AC2 25. LakinianzaalignAC2 mathbfc - mathbfa2 mathbfc - mathbfa cdot mathbfc - mathbfa mathbfc2 - 2 mathbfa cdot mathbfc mathbfa2 2R2 - 2 mathbfa cdot mathbfc,endalignambapo R ni circumradius. Kwa hivyo,mathbfa cdot mathbfc R2 - fracAC22.Vile vile, tunaweza kuthibitisha kwambamathbfa cdot mathbfb R2 - fracAB22.Kwa hiyo,mathbfa cdot mathbfc - mathbfa cdot mathbfb kushoto R2 - fracAC22 kulia - kushoto R2 - fracAB22 kulia fracAB2 - AC22 frac32 - 522 -8. 