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Giải bài 27 trang 92 sách bài tập toán 9 - Cánh diều tập 2

Cho tam giác ABC vuông tại A có đường cao AH = 2,4 cm và (frac{{AB}}{{AC}} = frac{3}{4}). Tính bán kính đường tròn nội tiếp r và bán kính đường tròn ngoại tiếp R của tam giác ABC.

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

Toán - Văn - Anh
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Đề bài

🦋Cho tam giác ABC vuông tại A có đường cao AH = 2,4 cm và \(\frac{{AB}}{{AC}} = \frac{3}{4}\). Tính bán kính đường tròn nội tiếp r và bán kính đường tròn ngoại tiếp R của tam giác ABC.

Phương pháp giải - Xem chi tiết

🐼Dựa vào dữ kiện đề bài để lập các tỉ số rồi tính bán kính đường tròn nội tiếp r và bán kính đường tròn ngoại tiếp R của tam giác ABC.

Lời giải chi tiết

Đặt AB = 3k (k > 0), suy ra AC = 4k (do \(\frac{{AB}}{{AC}} = \frac{3}{4}\)). Lại có tam giác ABC vuông tại A nên BC = 5k. Mặt khác BC.AH = AB. AC nên 5k . AH = 3k. 4k suy ra AH = 2,4k. Mà AH = 2,4 nên ta có 2,4k = 2,4 suy ra k = 1 nên AB = 3 cm, AC = 4 cm, BC = 5 cm. Mặt khác, do \(r = \frac{{AB + AC - BC}}{2},R = \frac{{BC}}{2}\) suy ra r = 1 cm và R = 2,5 cm.

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