如图,E是三角形ABCC的内心,AE的延长线交三角形三角形ABC的外接圆与D,求证 DE=DB=DC

已知,E是三角形ABC的内心,可得：∠DAB = ∠DAC ,∠EBA = ∠EBC .因为,∠DBE = ∠DBC+∠EBC = ∠DAC+∠EBC = ∠DAB+∠EBA = ∠DEB ,所以,DB = DE .因为,∠DAB = ∠DAC ,所以,DB = DC .综上可得：DE = DB = DC ....