Question

△ABC的三条角平分线交于点I(∠ACB>∠ABC),AI的延长线交BC于D,作IE⊥BC于E

∠BID=∠CIE正确么？,要过程

Answer 1

正确
∠BID＝∠IAB＋∠IBA＝1/2∠BAC＋1/2∠ABC＝1/2(∠BAC＋∠ABC)＝1/2(180°－∠ACB)＝90°－1/2∠ACB
而∠CIE＝90°－∠ICE＝90°－1/2∠ACB
∴∠BID＝∠CIE