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Giải bài 7 trang 82 sách bài tập toán 9 - Chân trời sáng tạo tập 2

Cho tứ giác ABCD nội tiếp đường tròn đường kính AD. Hai đường chéo AC và BD cắt nhau tại E. Vẽ EF vuông góc với AD tại F. Chứng minh ABEF và DCEF là hai tứ giác nội tiếp.

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

Toán - Văn - Anh
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Đề bài

🥂Cho tứ giác ABCD nội tiếp đường tròn đường kính AD. Hai đường chéo AC và BD cắt nhau tại E. Vẽ EF vuông góc với AD tại F. Chứng minh ABEF và DCEF là hai tứ giác nội tiếp.

Phương pháp giải - Xem chi tiết

Chứng minh tam giác ABE và tam giác AFE nội tiếp đường tròn đường kính AE. Từ đó suy ra ABEF nội tiếp đường tròn. Chứng minh tương tự với DCEF.

Lời giải chi tiết

Ta có \(\widehat {ABE} = {90^o}\)ꦰ (góc nội tiếp chắn nửa đường tròn); \(\widehat {AFE} = {90^o}\)(gt).

💝Tam giác ABE vuông tại B và tam giác AFE vuông tại F cùng nội tiếp đường tròn đường kính AE. Do đó, tứ giác ABEF nội tiếp đường tròn đường kính AE.

꧟Chứng minh tương tự, ta có tứ giác DCEF nội tiếp đường tròn đường kính DE.

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

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