如图,已知E是△ABC的内心,∠BAC的平分线交BC于点F,且与△ABC的外接圆相交于点D. (1)求证:∠DBE=∠DEB; (2)若AD=8cm,DF:FA=1:3.求DE的长.
问题描述:
如图,已知E是△ABC的内心,∠BAC的平分线交BC于点F,且与△ABC的外接圆相交于点D.
(1)求证:∠DBE=∠DEB;
(2)若AD=8cm,DF:FA=1:3.求DE的长.
答
(1)证明:∵E是△ABC的内心,∴∠ABE=∠CBE,∠BAD=∠CAD,∵∠CBD=∠CAD,∠DEB=∠BAD+∠ABE,∠DBE=∠CBD+∠EBC,∴∠DBE=∠DEB;(2)∵AD=8cm,DF:FA=1:3,∴DF=2,∵∠DBC=∠DAC,∠BAD=∠CAD,∴∠DBC=∠B...