<prompt> Acha overlineAD, overlineBE, overlineCF iwe miinuko ya pembetatu kali ABC. Ikiwa9 arrowoverrightarrowAD 4 overrightarrowBE 7 overrightarrowCF mathbf0,kisha ukokote angle ACB, kwa digrii.asyukubwa wa kitengo 0.6 cm;jozi A, B, C, D, E, F, H;A 2,5;B 0,0;C 8,0;D A tafakariB,CA2;E B tafakariC,AB2;F C tafakariA,BC2;kuchoraA--B--C--mzunguko;kuchoraA--D;kuchoraB--E;kuchoraC--F;leboA, A, N;leboB, B, SW;leboC, C, SE;leboD, D, S;leboE, E, NE;leboF, F, NW;asy  <response>: Acha H iwe kitovu cha pembetatu ABC. Tangu9 mshale wa kulia zaidiAD 4 mshale wa kulia zaidiBE 7 mshale uliopitilizaCF mathbf0,kuna pembetatu, sema PQR, kiasi kwamba overrightarrowPQ 9 overrightarrowAD, overrightarrowQR 4 overrightarrowBE, na overrightarrowRP 7 overrightarrowCF. Pembetatu PQR imeonyeshwa hapa chini, sio kiwango.asyukubwa wa kitengo 2 cm;jozi A, B, C, D, E, F, H, P, Q, R;B 0,0;C 3,0;A sehemu ya makutanoarcB,sqrt7,0,180,arcC,2,0,180;D A tafakariB,CA2;E B tafakariC,AB2;F C tafakariA,BC2;H uganiA, D, B, E;P A 2,0;Q P 9D - A9;R Q 4 E - B9;kuchoraA--B--C--mzunguko;kuchoraA--D;kuchoraB--E;kuchoraC--F;kuchoraP--Q--R--mzunguko;leboA, A, N;leboB, B, SW;leboC, C, SE;leboD, D, S;leboE, E, NE;leboF, F, NW;leboH, H, SW, Ondoa Kujaza;leboP, P, NW;leboQ, Q, SW;leboR, R, dir0;asyKwa kuwa angle AEB 90circ, angle ABE 90circ - A. Lakini angle BFH 90circ, hivyo angle BHF A. Tangu overline PR ni sambamba na overlineCF na overlineQR ni sambamba na overlineBE, angle PRQ A.Vile vile, tunaweza kuonyesha kwamba angle AHF B. Kwa kuwa overlinePQ ni sambamba na overlineAD, na overlinePR ni sambamba na overlineCF , angle QPR B. Kwa hivyo, pembetatu ABC na RPQ zinafanana. Hii inamaanishafracPQBC fracQRAC fracPRAB.Kishafrac9ADBC frac4BEAC frac7CFAB.Lakini AD frac2KBC, BE frac 2KAC, na CF frac2KAB, ambapo K ni eneo la pembetatu ABC, hivyofrac18KBC2 frac8KAC2 frac14KAB2.Kwa hiyo,fracBC29 fracAC24 fracAB27,hivyo BC:AC:AB 3:2: sqrt7.Hatimaye, kwa Sheria ya Cosines,cos C frac32 22 - 72 cdot 3 cdot 2 frac612 frac12,hivyo C 60circ. 