a, ke duong cao AH cua tam giac can ABC=> AH dong thoi la phan giac ^BAC va la trung truc BC

Lai co tam giac BDC deu => D thuoc trung truc BC

Suy ra A,D,H thang hang ( cung thuoc trung truc BC)

=> AD la phan giac ^BAC (trung voi AH)

b, Goi AD giao BM tai E

ta tinh duoc ^ABD= 20 do

=> ^EBD=10 do= ^EMA

=> tu giac ABDM noi tiep

=> EM.EB=ED.EA (1), ^AME=^BDE (3)

mat khac xet tam giac EAB co ^EAB=^EBA=10 do

=> tam giac EAB can tai E => EA=EB (2)

tu (1),(2), suy ra EM=ED (4)

co ^BED=^AEM doi dinh (5)

tu (3),(4),(5) suy ra tam giac EMA = tam giac EDB (g-c-g)

=> AM=BD=BC (tam giac BDC deu)

dpcm