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Lý thuyết Mở đầu về đường tròn Toán 9 Kết nối tri thức

1. Đường tròn

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

Toán - Văn - Anh
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1. Đường tròn

Định nghĩa đường tròn

Đường tròn tâm O bán kính R ﷽(R > 0), kí hiệu là (O; R), là hình gồm tất cả các điểm cách điểm O một khoảng bằng R.
Khi không cần để ý đến bán kính ta kí hiệu đường tròn tâm O là (O).

Điểm thuộc đường tròn

Nếu A là một điểm của đường tròn (O) thì ta viết \(A \in \left( O \right)\). Khi đó, ta còn nói đường  tròn (O) đi qua điểm A, hay điểm A nằm trên đường tròn (O).

Tổng quát:- Điểm A nằm trên đường tròn (O; R) nếu OA = R;- Điểm A nằm trong đường tròn (O; R) nếu OA < R;- Điểm A nằm ngoài đường tròn (O; R) nếu OA > R.

Hình tròn🎃 tâm O bán kính R là hình gồm các điểm nằm trên và nằm trong đường tròn (O;R).

2. Tính đối xứng của đường tròn

a) Đối xứng tâm

Hai điểm M và M’ gọi là đối xứng với nhau qua điểm I (hay qua tâm I) nếu I là trung điểm của đoạn MM’.

Ví dụ: Nếu O là giao điểm của hai đường chéo của hình bình hành ABCD thì

+) OA = OC nên A và C đối xứng với nhau.+) OB = OD nên B và D đối xứng với nhau.

b) Đối xứng trục

Hai điểm M và M’ gọi là đối xứng với nhau qua đường thẳng d (hay qua trục d) nếu d là đường trung trực của đoạn MM’.

Ví dụ: 🌟Nếu AH là đường cao trong tam giác ABC cân tại A thì AH cũng là đường trung trực của BC, nên B và C đối xứng với nhau qua AH.

c) Tâm đối xứng của đường tròn

- Đường tròn là hình có tâm đối xứng; tâm của đường tròn là tâm đối xứng của nó.

- Đường tròn có một tâm đối xứng.

d) Trục đối xứng của đường tròn

- Đường tròn là hình có trục đối xứng; mỗi đường thẳng qua tâm của đường tròn là một trục đối xứng của nó.

- Đường tròn có vô số trục đối xứng.

Quảng cáo

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

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