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Giải bài 3 trang 82 sách bài tập toán 9 - Chân trời sáng tạo tập 2

Cho hình thoi ABCD có cạnh bằng (asqrt 2 ) và nội tiếp đường tròn (O; R). Chứng minh ABCD là hình vuông và tính bán kính R theo a.

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

Toán - Văn - Anh
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Đề bài

🙈Cho hình thoi ABCD có cạnh bằng \(a\sqrt 2 \) và nội tiếp đường tròn (O; R). Chứng minh ABCD là hình vuông và tính bán kính R theo a.

Phương pháp giải - Xem chi tiết

Chứng minh ABCD là hình vuông nội tiếp đường tròn có bán kính bằng nửa đường chéo.

Lời giải chi tiết

Tứ giác ABCD là hình thoi nội tiếp đường tròn (O; R) nên \(\widehat A = \widehat C\)🐈 và \(\widehat A + \widehat C = {180^o}\), suy ra \(\widehat A = \widehat C = {90^o}\).

ꦐHình thoi ABCD có \(\widehat A = \widehat C = {90^o}\) nên là hình vuông.

ꦍKhi đó, hình vuông ABCD nội tiếp trong đường tròn có bán kính là \(R = \frac{{AB\sqrt 2 }}{2} = \frac{{a\sqrt 2 .\sqrt 2 }}{2} = a\)

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

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