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Giải bài tập 4 trang 82 SGK Toán 9 tập 1 - Chân trời sáng tạo

Cho tứ giác ABCD có (widehat B = widehat D = {90^o}). a) Chứng minh bốn điểm A, B, C, D cùng nằm trên một đường tròn. b) So sánh độ dài của AC và BD.

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 có \(\widehat B = \widehat D = {90^o}\).

꧅a) Chứng minh bốn điểm A, B, C, D cùng nằm trên một đường tròn.

b) So sánh độ dài của AC và BD.

Video hướng dẫn giải

Phương pháp giải - Xem chi tiết

a) - Sử dụng tính chất đường trung tuyến ứng với cạnh huyền bằng một nửa cạnh huyền.

⛦- Chứng mình A, B, C, D cách đều 1 điểm nên nằm trên 1 đường tròn.

b) Dựa vào quan hệ giữa đường kính và dây cung.

Lời giải chi tiết

a) Gọi O là trung điểm của AC.

🎃Xét tam giác ABC vuông tại B có O là trung điểm của AC nên \(OA = OB = OC = \frac{1}{2} AC\)

💝Xét tam giác ADC vuông tại D có O là trung điểm của AC nên \(OA = OD = OC = \frac{1}{2} AC\)

♍Suy ra \(OA = OB = OC = OD = \frac{1}{2} AC\) nên A, B, C, D cùng nằm trên một đường tròn tâm O đường kính AC.

ꦰb) Xét đường tròn tâm O đường kính AC có BD là dây cung không đi qua tâm O nên AC > BD.

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

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