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Giải bài tập 5.27 trang 107 SGK Toán 9 tập 1 - Kết nối tri thức

Cho hai đường tròn (O) và (O’) tiếp xúc ngoài với nhau tại A. Một đường thẳng qua A cắt (O) tại B và cắt (O’) tại C. Chứng minh rằng OB // O’C.

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

Toán - Văn - Anh
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Đề bài

Cho hai đường tròn (O) và (O’) tiếp xúc ngoài với nhau tại A. Một đường thẳng qua A cắt (O) tại B và cắt (O’) tại C. Chứng minh rằng OB // O’C.

Video hướng dẫn giải

Phương pháp giải - Xem chi tiết

Dựa vào tính chất của tam giác cân và hai góc đối đỉnh suy ra \(\widehat {{\rm{OBA}}} = \widehat {{\rm{O'CA}}}\) Khi đó OB // O’C.

Lời giải chi tiết

Vì OA = OB nên tam giác OAB cân tại O. Suy ra: \(\widehat {{\rm{OBA}}} = \widehat {{\rm{OAB}}}\) Vì O’A = O’C nên tam giác O’AC cân tại O. Suy ra: \(\widehat {{\rm{O'AC}}} = \widehat {{\rm{O'CA}}}\) Lại có: \(\widehat {{\rm{OAB}}} = \widehat {{\rm{O'AB}}}\) Suy ra: \(\widehat {{\rm{OBA}}} = \widehat {{\rm{O'CA}}}\) Vậy OB // O’C.

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

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