<prompt> Katika pembetatu ABC, wastani overlineAD na overlineBE ni perpendicular. Ikiwa AC 22 na BC 31, basi pata AB.  <response>: Tunayo D na E ndio viini vya overlineBC na overlineAC, mtawalia, kwa hivyooverrightarrowD fracoverrightarrowB overrightarrowC2 quad textna quad overrightarrowE fracoverrightarrowA overrightarrowC2.asyukubwa wa kitengo cm 0.2;jozi A, B, C, D, E;B 0,0;C 31,0;A sehemu ya makutanoarcB,17,0,180,arcC,22,0,180;D B C2;E A C2;kuchoraA--B--C--mzunguko;kuchoraA--D;kuchoraB--E;leboA, A, N;leboB, B, SW;leboC, C, SE;leboD, D, S;leboE, E, NE;asyPia, overrightarrowAD cdot overrightarrowBE 0, auleft overrightarrowA - fracoverrightarrowB overrightarrowC2 kulia cdot left overrightarrowB - fracoverrightarrowA overrightarrowC2 kulia 0.Kuzidisha kila kipengele kwa 2 ili kuondoa sehemu, tunapata2 arrowoverrightarrowA - overrightarrowB - overrightarrowC cdot 2 overrightarrowB - overrightarrowA - overrightarrowC 0.Kupanua bidhaa ya nukta, tunapata-2 arrowoverrightarrowA cdot overrightarrowA - 2 overrightarrowB cdot overrightarrowB overrightarrowC cdot overrightarrowC 5 overrightarrowA cdoti mshale uliopitilizaB - mshale wa kulia zaidiA cdot mshale wa kuliaC - mshale uliopitilizaB cdot overrightarrowC 0.Kuweka kipenyo cha pembetatu ABC kuwa asili , na kutumia kile tunachojua kuhusu bidhaa hizi za nukta, kama overrightarrowA cdot overrightarrowB R2 - fracc22, tunapata-2R2 - 2R2 R2 5 kushoto R2 - fracc22 kulia - kushoto R2 - fracb2 2 kulia - kushoto R2 - fraca22 kulia 0.Hii hurahisisha hadi a2 b2 5c2.Tumepewa kwamba a 31 na b 22, hivyo 5c2 312 222 1445, na c 17. 