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Giải bài tập 9.7 trang 76 SGK Toán 9 tập 2 - Kết nối tri thức

Cho đường tròn (O) ngoại tiếp tam giác ABC. Tính bán kính của (O), biết rằng tam giác ABC vuông cân tại A và có cạnh bên bằng (2sqrt 2 cm).

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

Toán - Văn - Anh
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Đề bài

Cho đường tròn (O) ngoại tiếp tam giác ABC. Tính bán kính của (O), biết rằng tam giác ABC vuông cân tại A và có cạnh bên bằng \(2\sqrt 2 cm\).

Video hướng dẫn giải

Phương pháp giải - Xem chi tiết

+ Áp dụng định lí Pythagore vào tam giác ABC vuông tại A tính BC. + Vì O là trung điểm của BC nên \(OB = OC = \frac{{BC}}{2}\) là bán kính đường tròn (O) ngoại tiếp tam giác ABC.

Lời giải chi tiết

Tam giác ABC vuông cân tại A nên \(AB = AC = 2\sqrt 2 cm\) Áp dụng định lí Pythagore vào tam giác ABC vuông tại A ta có: \(B{C^2} = A{B^2} + A{C^2} = {\left( {2\sqrt 2 } \right)^2} + {\left( {2\sqrt 2 } \right)^2} = 16 \) suy ra \(BC = 4cm\) Vì O là trung điểm của BC nên \(OB = OC = \frac{{BC}}{2} = \frac{4}{2} = 2\left( {cm} \right)\) Vì tam giác ABC vuông tại A nên tam giác ABC nội tiếp đường tròn tâm O, bán kính OC. Vậy bán kính đường tròn (O) ngoại tiếp tam giác ABC bằng 2cm.

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