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Giải bài 3 trang 88 vở thực hành Toán 9 tập 2

Cho đường tròn (O) và hai dây cung AC, BD cắt nhau tại X như hình bên. Tính số đo góc AXB biết rằng (widehat {ADB} = {30^o},widehat {DBC} = {50^o}).

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

Toán - Văn - Anh
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Đề bài

Cho đường tròn (O) và hai dây cung AC, BD cắt nhau tại X như hình bên. Tính số đo góc AXB biết rằng \(\widehat {ADB} = {30^o},\widehat {DBC} = {50^o}\).

Phương pháp giải - Xem chi tiết

+ Do \(\widehat {DAC}\) và \(\widehat {DBC}\) là góc nội tiếp cùng chắn cung DC của (O) nên \(\widehat {DAC} = \widehat {DBC}\). + Vì tổng ba góc trong tam giác ADX bằng \({180^o}\) và góc AXB kề bù với góc AXD nên  \(\widehat {AXB} = {180^o} - \widehat {AXD} = \widehat {XAD} + \widehat {ADX}\).

Lời giải chi tiết

Do \(\widehat {DAC}\) và \(\widehat {DBC}\) là góc nội tiếp cùng chắn cung DC của (O) nên \(\widehat {DAC} = \widehat {DBC} = {50^o}\). Vì tổng ba góc trong tam giác ADX bằng \({180^o}\) và góc AXB kề bù với góc AXD nên  \(\widehat {AXB} = {180^o} - \widehat {AXD} = \widehat {XAD} + \widehat {ADX} = {30^o} + {50^o} = {80^o}\).

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

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