Cho ΔMBC nhọn (AB < AC) nội tiếp đường tròn (O). Các đường cao AD, BE, CF cắt nhau tại H. Đường thẳng EF cắt đường thẳng BC tại M và đường thẳng AM cắt đường tròn (O) tại điểm L (L khác A). Chứng minh rằng: BFHD là tứ giác nội tiếp; H là tâm đường tròn nội tiếp ADEF

giúp = 200 xu
câu b,c<!--[if gte msEquation 12]> 107%;font-family:"Cambria Math",serif;mso-fareast-font-family:Calibri;
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∆ABC nhọn font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";
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tiếp đường
tròn font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";
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mso-fareast-theme-font:minor-latin;mso-bidi-font-family:"Times New Roman";
mso-ansi-language:EN-US;mso-fareast-language:EN-US;mso-bidi-language:AR-SA'>.
Các đường
cao AD, BE,
CF cắt nhau
tại H. Đường
thẳng EF cắt
đường thẳng
BC tại M
và đường thẳng
AM cắt đường
tròn font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";
mso-hansi-font-family:"Cambria Math";mso-bidi-font-family:"Times New Roman"; font-style:italic;mso-bidi-font-style:normal'> line-height:107%;font-family:"Cambria Math",serif;mso-fareast-font-family:
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mso-fareast-theme-font:minor-latin;mso-bidi-font-family:"Times New Roman";
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L 14.0pt;mso-ansi-font-size:14.0pt;mso-bidi-font-size:14.0pt;font-family:
"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";mso-hansi-font-family:
"Cambria Math";mso-bidi-font-family:"Times New Roman";font-style:italic; mso-bidi-font-style:normal'> line-height:107%;font-family:"Cambria Math",serif;mso-fareast-font-family:
Calibri;mso-fareast-theme-font:minor-latin;mso-bidi-font-family:"Times New Roman";
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mso-fareast-theme-font:minor-latin;mso-bidi-font-family:"Times New Roman";
mso-ansi-language:EN-US;mso-fareast-language:EN-US;mso-bidi-language:AR-SA'>.
Chứng minh
rằng:<!--[endif]--><!--[if gte vml 1]--> coordsize="21600,21600" o:spt="75" o:preferrelative="t" path="m@4@5l@4@11@9@11@9@5xe"
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mso-fareast-theme-font:minor-latin;mso-bidi-font-family:"Times New Roman";
mso-ansi-language:EN-US;mso-fareast-language:EN-US;mso-bidi-language:AR-SA'>Cho
∆ABC nhọn font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";
mso-hansi-font-family:"Cambria Math";mso-bidi-font-family:"Times New Roman"; font-style:italic;mso-bidi-font-style:normal'> line-height:107%;font-family:"Cambria Math",serif;mso-fareast-font-family:
Calibri;mso-fareast-theme-font:minor-latin;mso-bidi-font-family:"Times New Roman";
mso-ansi-language:EN-US;mso-fareast-language:EN-US;mso-bidi-language:AR-SA'> AB<AC
mso-fareast-font-family:Calibri;mso-fareast-theme-font:minor-latin;
mso-bidi-font-family:"Times New Roman";mso-ansi-language:EN-US;mso-fareast-language:
EN-US;mso-bidi-language:AR-SA'> nội
tiếp đường
tròn font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";
mso-hansi-font-family:"Cambria Math";mso-bidi-font-family:"Times New Roman"; font-style:italic;mso-bidi-font-style:normal'> line-height:107%;font-family:"Cambria Math",serif;mso-fareast-font-family:
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mso-fareast-theme-font:minor-latin;mso-bidi-font-family:"Times New Roman";
mso-ansi-language:EN-US;mso-fareast-language:EN-US;mso-bidi-language:AR-SA'>.
Các đường
cao AD, BE,
CF cắt nhau
tại H. Đường
thẳng EF cắt
đường thẳng
BC tại M
và đường thẳng
AM cắt đường
tròn font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";
mso-hansi-font-family:"Cambria Math";mso-bidi-font-family:"Times New Roman"; font-style:italic;mso-bidi-font-style:normal'> line-height:107%;font-family:"Cambria Math",serif;mso-fareast-font-family:
Calibri;mso-fareast-theme-font:minor-latin;mso-bidi-font-family:"Times New Roman";
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mso-fareast-theme-font:minor-latin;mso-bidi-font-family:"Times New Roman";
mso-ansi-language:EN-US;mso-fareast-language:EN-US;mso-bidi-language:AR-SA'>tại
L 14.0pt;mso-ansi-font-size:14.0pt;mso-bidi-font-size:14.0pt;font-family:
"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";mso-hansi-font-family:
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Calibri;mso-fareast-theme-font:minor-latin;mso-bidi-font-family:"Times New Roman";
mso-ansi-language:EN-US;mso-fareast-language:EN-US;mso-bidi-language:AR-SA'> L≠A 107%;font-family:"Cambria Math",serif;mso-fareast-font-family:Calibri;
mso-fareast-theme-font:minor-latin;mso-bidi-font-family:"Times New Roman";
mso-ansi-language:EN-US;mso-fareast-language:EN-US;mso-bidi-language:AR-SA'>.
Chứng minh
rằng:<!--[endif]--><!--[if gte vml 1]--> coordsize="21600,21600" o:spt="75" o:preferrelative="t" path="m@4@5l@4@11@9@11@9@5xe"
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o:title="" chromakey="white"/>
<!--[endif]--><!--[if gte msEquation 12]--> 107%;font-family:"Cambria Math",serif;mso-fareast-font-family:Calibri;
mso-fareast-theme-font:minor-latin;mso-bidi-font-family:"Times New Roman";
mso-ansi-language:EN-US;mso-fareast-language:EN-US;mso-bidi-language:AR-SA'>Cho
∆ABC nhọn font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";
mso-hansi-font-family:"Cambria Math";mso-bidi-font-family:"Times New Roman"; font-style:italic;mso-bidi-font-style:normal'> line-height:107%;font-family:"Cambria Math",serif;mso-fareast-font-family:
Calibri;mso-fareast-theme-font:minor-latin;mso-bidi-font-family:"Times New Roman";
mso-ansi-language:EN-US;mso-fareast-language:EN-US;mso-bidi-language:AR-SA'> AB<AC
mso-fareast-font-family:Calibri;mso-fareast-theme-font:minor-latin;
mso-bidi-font-family:"Times New Roman";mso-ansi-language:EN-US;mso-fareast-language:
EN-US;mso-bidi-language:AR-SA'> nội
tiếp đường
tròn font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";
mso-hansi-font-family:"Cambria Math";mso-bidi-font-family:"Times New Roman"; font-style:italic;mso-bidi-font-style:normal'> line-height:107%;font-family:"Cambria Math",serif;mso-fareast-font-family:
Calibri;mso-fareast-theme-font:minor-latin;mso-bidi-font-family:"Times New Roman";
mso-ansi-language:EN-US;mso-fareast-language:EN-US;mso-bidi-language:AR-SA'>O 107%;font-family:"Cambria Math",serif;mso-fareast-font-family:Calibri;
mso-fareast-theme-font:minor-latin;mso-bidi-font-family:"Times New Roman";
mso-ansi-language:EN-US;mso-fareast-language:EN-US;mso-bidi-language:AR-SA'>.
Các đường
cao AD, BE,
CF cắt nhau
tại H. Đường
thẳng EF cắt
đường thẳng
BC tại M
và đường thẳng
AM cắt đường
tròn font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";
mso-hansi-font-family:"Cambria Math";mso-bidi-font-family:"Times New Roman"; font-style:italic;mso-bidi-font-style:normal'> line-height:107%;font-family:"Cambria Math",serif;mso-fareast-font-family:
Calibri;mso-fareast-theme-font:minor-latin;mso-bidi-font-family:"Times New Roman";
mso-ansi-language:EN-US;mso-fareast-language:EN-US;mso-bidi-language:AR-SA'>O 107%;font-family:"Cambria Math",serif;mso-fareast-font-family:Calibri;
mso-fareast-theme-font:minor-latin;mso-bidi-font-family:"Times New Roman";
mso-ansi-language:EN-US;mso-fareast-language:EN-US;mso-bidi-language:AR-SA'>tại
L 14.0pt;mso-ansi-font-size:14.0pt;mso-bidi-font-size:14.0pt;font-family:
"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";mso-hansi-font-family:
"Cambria Math";mso-bidi-font-family:"Times New Roman";font-style:italic; mso-bidi-font-style:normal'> line-height:107%;font-family:"Cambria Math",serif;mso-fareast-font-family:
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mso-fareast-theme-font:minor-latin;mso-bidi-font-family:"Times New Roman";
mso-ansi-language:EN-US;mso-fareast-language:EN-US;mso-bidi-language:AR-SA'>.
Chứng minh
rằng:<!--[endif]--><!--[if gte vml 1]--> coordsize="21600,21600" o:spt="75" o:preferrelative="t" path="m@4@5l@4@11@9@11@9@5xe"
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height:14.25pt'>
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<!--[endif]-->----- Nội dung dịch tự động từ ảnh -----
Câu 4. (3,0 điểm) Cho MBC nhọn (AB < AC) nội tiếp đường tròn (O). Các đường cao AD, BE, CF cắt
nhau tại H. Đường thẳng EF cắt đường thẳng BC tại M và đường thẳng AM cắt đường tròn (O) tại điểm
L (L * 4). Chứng minh rằng:
a) BFHD là tứ giác nội tiếp.
b) . H là tâm đường tròn nội tiếp ADEF .
MF
AC DB
ME
AB¹ DC