A B ⊥ I H A B ⊥ A C = > I H / / A C A C ⊥ K H = > I H ⊥ K H AB \perp IH\\ AB \perp AC\\ =>IH//AC\\ AC \perp KH\\ =>IH \perp KH A B ⊥ I H A B ⊥ A C = > I H / / A C A C ⊥ K H = > I H ⊥ K H
Δ A I H \Delta AIH Δ A I H A D AD A D H I HI H I
= > Δ A I H =>\Delta AIH = > Δ A I H A A A
= > A 1 ^ = A 2 ^ =>\widehat{A_1}=\widehat{A_2} = > A 1 = A 2
Tương tự với Δ A K H \Delta AKH Δ A K H
= > A 3 ^ = A 4 ^ =>\widehat{A_3}=\widehat{A_4} = > A 3 = A 4
Tứ giác A D H E ADHE A D H E
D A E ^ = 36 0 o − 3.9 0 o = 9 0 o < = > A 2 ^ + A 3 ^ = 9 0 o < = > 2 ( A 2 ^ + A 3 ^ ) = 18 0 o < = > A 1 ^ + A 2 ^ + A 3 ^ + A 4 ^ = 18 0 o < = > I A K ^ = 18 0 o \widehat{DAE}=360^o-3.90^o=90^o\\ <=>\widehat{A_2}+\widehat{A_3}=90^o\\ <=>2(\widehat{A_2}+\widehat{A_3})=180^o\\ <=>\widehat{A_1}+\widehat{A_2}+\widehat{A_3}+\widehat{A_4}=180^o\\ <=>\widehat{IAK}=180^o D A E = 3 6 0 o − 3 . 9 0 o = 9 0 o < = > A 2 + A 3 = 9 0 o < = > 2 ( A 2 + A 3 ) = 1 8 0 o < = > A 1 + A 2 + A 3 + A 4 = 1 8 0 o < = > I A K = 1 8 0 o
Hay ba điểm I , A , K I,A,K I , A , K
