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Giải bài 9.17 trang 53 sách bài tập toán 9 - Kết nối tri thức tập 2

Cho tam giác nhọn ABC nội tiếp đường tròn (O). Cho điểm M trên cạnh BC của tam giác ABC và điểm D trên cung nhỏ BC của (O) sao cho (widehat {BAD} = widehat {MAC}). Chứng minh rằng $Delta AMBbacksim Delta ACD$.

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

Toán - Văn - Anh
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Đề bài

Cho tam giác nhọn ABC nội tiếp đường tròn (O). Cho điểm M trên cạnh BC của tam giác ABC và điểm D trên cung nhỏ BC của (O) sao cho \(\widehat {BAD} = \widehat {MAC}\). Chứng minh rằng $\Delta AMB\backsim \Delta ACD$.

Phương pháp giải - Xem chi tiết

Chứng minh \(\widehat {ABM} = \widehat {ADC}\), \(\widehat {BAM} = \widehat {DAC}\), suy ra $\Delta AMB\backsim \Delta ACD$ (g. g).

Lời giải chi tiết

Hai tam giác AMB và tam giác ACD có: \(\widehat {ABM} = \widehat {ADC}\) (hai góc nội tiếp đường tròn (O) cùng chắn cung nhỏ AC) \(\widehat {BAM} = \widehat {BAC} - \widehat {MAC} = \widehat {BAC} - \widehat {BAD} = \widehat {DAC}\) Do đó, $\Delta AMB\backsim \Delta ACD$ (g. g).

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

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