<prompt> Katika pembetatu ABC, pembe C90circ, AC6 na BC8. Alama D na E ziko kwenye overlineAB na overlineBC, mtawalia, na angle BED90circ. Ikiwa DE4, basi urefu wa BD ni upi? asykuagiza olympiad; kuagiza jiometri; ukubwa 150; defaultpenlinewidth0.8;kuchoraasili--6,0--6,8--mzunguko;chora2,83--6,83;nuktaA,asili,SW; nuktaB,6,8,NE; nuktaC,6,0,SE; nuktaD,2,83,W; nuktaE,6,83,E;choraalama ya kulia6,8,6,83,2,83,12;choraalama ya kulia6,8,6,0,asili,12;asy  <response>: Kutumia Nadharia ya Pythagorean kwa pembetatu ABC kunatoa BA10. Tangu pembetatu DBEsimpembetatu ABC, fracBDBAfracDEAC.qquadrm SoqquadBDfracDEACBAfrac 4610frac203. 