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Tính bán kính đường tròn ngoại tiếp tam giác ABC vuông tại A với AB = 5cm, AC = 12cm.

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Đề bài

Tính bán kính đường tròn ngoại tiếp tam giác ABC vuông tại A với AB = 5cm, AC = 12cm.

Video hướng dẫn giải

Phương pháp giải - Xem chi tiết

Áp dụng định lý: Tâm đường tròn ngoại tiếp tam giác vuông là trung điểm của cạnh huyền và bán kính bằng nửa cạnh huyền của tam giác vuông đó.

Lời giải chi tiết

Gọi (O) là đường tròn ngoại tiếp tam giác ABC. Xét tam giác ABC vuông tại A có: \(\begin{array}{l}B{C^2} = A{B^2} + A{C^2}(Pytago)\\B{C^2} = {5^2} + {12^2}\\B{C^2} = 169\\BC = 13cm\end{array}\) Vì ABC vuông tại A nên tâm O của đường tròn ngoại tiếp là trung điểm của cạnh huyền BC (định lý) Vậy bán kính \(OB = OC = \frac{{BC}}{2} = \frac{{13}}{2}cm.\)

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