<prompt> pembetatu DEF imeandikwa ndani ya pembetatu ABC kiasi kwamba D,E,F ziko kwenye BC, AC, AB, mtawalia. Miduara ya pembetatu DEC, pembetatu BFD, pembetatu AFE ina vituo O_1,O_2,O_3, mtawalia. Pia, AB 23, BC 25, AC24, na stackrelfrownBF stackrelfrownEC, stackrelfrownAF stackrelfrownCD, stackrelfrownAE stackrelfrownBD. Urefu wa BD unaweza kuandikwa katika muundo frac mn, ambapo m na n ni nambari kamili kuu kiasi. Tafuta mn.  <response>: asy ukubwa 150; defaultpenlinewidth0.8; alama za kuagiza; jozi B 0,0, C 25,0, A 57850,19.8838; kuchoraA--B--C--mzunguko; leboB,B,SW; leboC,C,SE; leboA,A,N; jozi D 13,0, E 11A 13C24, F 12B 11A23; kuchoraD--E--F--mzunguko; leboD,D,dir-90; leboE,E,dir0; leboF,F,dir180; choraA--E,StickIntervalMarker1,3,size6;choraB--D,StickIntervalMarker1,3,size6; kuchoraF--B,StickIntervalMarker1,2,size6; kuchoraE--C,StickIntervalMarker1,2,size6; kuchoraA--F,StickIntervalMarker1,1,size6; kuchoraC--D,StickIntervalMarker1,1,size6; lebo24,A--C,5dir0; lebo25,B--C,5dir-90; lebo23,B--A,5dir180; asyKutoka pande za karibu, mahusiano yafuatayo yanaweza kupatikana:anzaalign DC EC 1 AE AF 1 BD BF 2 mwishoalignKwa kuwa BF EC, na DC BF 1, BD DC 1. Hivyo, BC BD DC BD BD - 1 . 26 2BD. Hivyo, BD 131. Hivyo, jibu ni 14. 