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Cách tính độ dài đoạn thẳng, góc liên quan đến tiếp tuyến của đường tròn - Toán 9

1. Khái niệm Tiếp tuyến của đường tròn

Nếu đường thẳng và đường tròn tiếp xúc nhau thì đường thẳng được gọi là tiếp tuyến của đường tròn, điểm chung được gọi là tiếp điểm.

Điểm chung H của đường thẳng và đường tròn tiếp xúc với nhau goi là tiếp điểm.

Khi đó đường thẳng a còn gọi là tiếp tuyến của đường tròn (O) tại H.

Đường thẳng a tiếp xúc với đường tròn (O) tại H thì \(OH \bot a\).

2. Cách chứng minh một đường thẳng là tiếp tuyến của đường tròn

Để chứng minh đường thẳng d là tiếp tuyến của đường tròn (O;R) tại tiếp điểm A, ta có thể làm theo cách sau:

Cách 1. Chứng minh \(OA \bot d\) tại A và \(A \in \left( O \right)\).

Cách 2. Vẽ \(OH \bot d\). Chứng minh \(OH \equiv OA = R\).

Cách 3. Vẽ tiếp tuyến \(d'\) của \(\left( O \right)\). Ta chứng minh \(d \equiv d'\).

3. Cách tính độ dài đoạn thẳng, góc liên quan đến tiếp tuyến của đường tròn

Vận dụng kiến thức về tiếp tuyến và hệ thức lượng trong tam giác vuông để tính toán.

4. Bài tập vận dụng

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