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Lý thuyết Tứ giác nội tiếp Toán 9 Kết nối tri thức

1. Đường tròn ngoại tiếp của một tứ giác Định nghĩa đường tròn ngoại tiếp tứ giác Tứ giác có bốn đỉnh nằm trên một đường tròn được gọi là tứ giác nội tiếp đường tròn (hoặc đơn giản là tứ giác nội tiếp) và đường tròn được gọi là đường tròn ngoại tiếp tứ giác.

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

Toán - Văn - Anh
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1. Đường tròn ngoại tiếp của một tứ giác

Định nghĩa đường tròn ngoại tiếp tứ giác

Tứ giác có bốn đỉnh nằm trên một đường tròn được gọi là tứ giác nội tiếp đường tròn (hoặc đơn giản là tứ giác nội tiếp) và đường tròn được gọi là đường tròn ngoại tiếp tứ giác.

Ví dụ:

Tứ giác ABCD là tứ giác nội tiếp và đường tròn (O) được gọi là đường tròn ngoại tiếp tứ giác ABCD.

Tính chất

Trong một tứ giác nội tiếp đường tròn, tổng số đo hai góc đối bằng \(180^\circ \).

Ví dụ:

Tứ giác ABCD nội tiếp (O) nên \(\widehat A + \widehat C = 180^\circ ;\widehat B + \widehat D = 180^\circ \).

2. Đường tròn ngoại tiếp hình chữ nhật và hình vuông

Hình chữ nhật và hình vuông là các tứ giác nội tiếp. Đường tròn ngoại tiếp của chúng có tâm là giao điểm của hai đường chéo và bán kính bằng một nửa độ dài đường chéo.

Ví dụ:

Áp dụng định lí Pythagore cho tam giác ABD vuông tại A, ta có:\(B{D^2} = A{B^2} + A{D^2} = {3^2} + {4^2} = 25\) nên \(BD = 5cm\).Do đó, ta có \(R = \frac{{BD}}{2} = 2,5cm\).Đường tròn (O;2,5) là đường tròn ngoại tiếp hình chữ nhật ABCD.

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