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Giải bài 3 trang 92 sách bài tập toán 9 - Chân trời sáng tạo tập 1

Hai tiếp tuyến tại A và B của đường tròn (O) cắt nhau tại M và (widehat {AMB} = {35^o}). a) Tính số đo của góc ở tâm tạo bởi hai bán kính OA, Ob. b) Tính số đo mỗi cung (oversetfrown{AB}) (cung lớn và cung nhỏ).

Tổng hợp Đề thi vào 10 có đáp án và lời giải

Toán - Văn - Anh
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Đề bài

🌺Hai tiếp tuyến tại A và B của đường tròn (O) cắt nhau tại M và \(\widehat {AMB} = {35^o}\).

🌞a) Tính số đo của góc ở tâm tạo bởi hai bán kính OA, OB.

🥃b) Tính số đo mỗi cung \(\overset\frown{AB}\) (cung lớn và cung nhỏ).

Phương pháp giải - Xem chi tiết

Dựa vào: Số đo của cung nhỏ bằng số đo của góc ở tâm chắn cung đó. Số đo của cung lớn bằng hiệu giữa 360oౠ và số đo cung nhỏ có chung hai đầu mút với cung lớn.

Lời giải chi tiết

a) Vì MA, MB là hai tiếp tuyến của (O) cắt nhau tại M nên \(\widehat {OAM} = {90^o},\widehat {MBO} = {90^o}\). Xét tứ giác AOBM, ta có: \(\widehat {OAM} + \widehat {OBM} + \widehat {AMB} + \widehat {AOB} = {360^o}\) Hay \({90^o} + {90^o} + {35^o} + \widehat {AOB} = {360^o}\) suy ra \(\widehat {AOB} = {145^o}\).

b) Vì \(\widehat {AOB} = {145^o}\) nên số đo cung nhỏ \(\overset\frown{AB}\) là 145o, số đo cung lớn \(\overset\frown{AB}\) là 360o – 145o = 215o.

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Tham Gia Group Dành Cho Lớp 9 - Ôn Thi Vào Lớp 10 Miễn Phí

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