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Giải bài 15 trang 90 sách bài tập toán 9 - Cánh diều tập 2

Ở Hình 13, hai đường tròn (O), (O’) giao nhau tại A, B và CD là một dây cung của (O). Tia CA cắt (O’) tại E và tia DB cắt (O’) tại F. Chứng minh EF song song với CD.

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

Toán - Văn - Anh
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Đề bài

🤡Ở Hình 13, hai đường tròn (O), (O’) giao nhau tại A, B và CD là một dây cung của (O). Tia CA cắt (O’) tại E và tia DB cắt (O’) tại F. Chứng minh EF song song với CD.

 

Phương pháp giải - Xem chi tiết

Trong một tứ giác nội tiếp đường tròn, tổng số đo hai góc đối bằng 180o.

Lời giải chi tiết

Ta có tứ giác ABCD nội tiếp đường tròn (O) nên \(\widehat {ACD} = \widehat {ABF}( = {180^o} - \widehat {ABD})\)  (1). Mặt khác, tứ giác ABFE nội tiếp đường tròn (O’) suy ra \(\widehat {ABF} + \widehat {AEF} = {180^o}\) (2). Từ (1) và (2) ta có \(\widehat {ACD} + \widehat {AEF} = {180^o}\) hay \(\widehat {ECD} + \widehat {CEF} = {180^o}\). Suy ra EF // CD.

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

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