已知△ABC的两条角平分线BD,CE交于点I,ID=IE,∠ABC=70度,则∠A=_百 ...答:∠A=40° 过I点分别作IL,IP,IK垂直于AB,BC,AC.∵IL,IP,IK全过I点,ID=IE,∠ILB=∠IPB=90°。IB=IB,∠LBI=∠PBI,∴△BLI≌△BPI,∴IL=IP,∵CI是∠BCA的平分线,∴∠ICB=∠ICE,又∵IP垂直于IE,∴∠IPC=90°,∠IEC=90°,∴∠IPC=∠IEC,∴△CPI≌△IEC。∴IP=IE。易证...
已知三角形ABC的两条内角平分线BD,CF交于点I,ID=IE,若角ABC=70度,则...答:∠A=40° 过I点分别作IL,IP,IK垂直于AB,BC,AC.∵IL,IP,IK全过I点,ID=IE,∠ILB=∠IPB=90°。IB=IB,∠LBI=∠PBI,∴△BLI≌△BPI,∴IL=IP,∵CI是∠BCA的平分线,∴∠ICB=∠ICE,又∵IP垂直于IE,∴∠IPC=90°,∠IEC=90°,∴∠IPC=∠IEC,∴△CPI≌△IEC。∴IP=IE。易证...