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Giải bài 6 trang 82 sách bài tập toán 9 - Chân trời sáng tạo tập 2

Cho hình vuông ABCD và điểm M bất kì trên cạnh BC (M khác B và C). Qua B kẻ đường thẳng vuông góc với DM tại H. Chứng minh BHCD là tứ giác nội tiếp. Xác định tâm I của đường tròn ngoại tiếp tứ giác BHCD.

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

Toán - Văn - Anh
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Đề bài

🃏Cho hình vuông ABCD và điểm M bất kì trên cạnh BC (M khác B và C). Qua B kẻ đường thẳng vuông góc với DM tại H. Chứng minh BHCD là tứ giác nội tiếp. Xác định tâm I của đường tròn ngoại tiếp tứ giác BHCD.

Phương pháp giải - Xem chi tiết

Chứng minh tam giác BHD và tam giác BCD nội tiếp đường tròn đường kính BD. Từ đó suy ra BHCD nội tiếp đường tròn 🐭đường kính BD. Suy ra I là tâm của đường tròn ngoại tiếp tứ giác BHCD.

Lời giải chi tiết

Ta có \(\widehat {BCD} = {90^o}\)(gt); \(\widehat {BHD} = {90^o}\)(gt).

⭕Tam giác BHD vuông tại H và tam giác BCD vuông tại C cùng nội tiếp đường tròn đường kính BD.

𝄹Do đó, tứ giác BHCD nội tiếp đường tròn đường kính BD.

💯Gọi I là trung điểm của BD, khi đó I là tâm của đường tròn ngoại tiếp tứ giác BHCD.

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

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