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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 k𝕴ính OA, OB.

b) Tính số 🌊đ💮o 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 360o và số đo cung nhỏ có chung ha♎i 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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