<prompt> Katika pembetatu ABC, AB 13, BC 15, na CA 14. Pointi D iko kwenye overlineBC na CD 6. Pointi E iko kwenye overlineBC kiasi kwamba angle BAE angle CAD. Tafuta BE.  <response>: Acha alpha pembe BAE pembe CAD, na uruhusu betaangle EAD. KishaBDoverDC ABDoverADC frac12 cdot ABcdot ADsin angle BAD overfrac12 cdot ADcdot ACsin angle CAD ABoverACcdotsinalphabetaover sinalpha.Vile vile, BEoverECABoverACcdotsin angle BAEoversin pembe CAE ABoverAC cdotsinalpha oversinalphabeta,na hivyo BE zaidi yaECAB2cdot DCoverAC2cdot BD.Kubadilisha thamani zilizotolewa inatoa BEEC132cdot614 2cdot9169294. Kwa hiyo,BE frac15cdot169169294 frac2535463.asyjozi A,B,C,D,I;B0,0;C15,0;A5,12;D9,0;I6,0;choraA--B--C--mzunguko,upana wa mstari0.7;choraI--A--D,upana wa mstari0.7;lebo13,2.5,6.5,W;lebo14,10,6.5,E;lebo15,7.5,-2,S;lebo6,12,0,S;chora0,-1.7--15,-1.7,Mishale6;leboB,B,S;leboC,C,S;leboD,D,S;leboE,I,S;leboA,A,N;leboalpha,4.5,10,S;leboalpha,6.5,10,S;lebobeta,5.7,9,S;asy 