📚 Circle Theorems | 圆定理
Circle theorems are a fundamental part of the IGCSE Mathematics Extended syllabus. They describe how angles, chords, tangents, and radii relate to one another inside a circle. In the exam, you are expected not only to calculate missing angles but also to justify each step using the correct theorem. This article explains the most important theorems, common problems, and exam strategies.
圆定理是 IGCSE 数学扩展课程的基础内容，它描述了圆内角、弦、切线与半径之间的关系。考试中不仅要求计算未知角度，还要求用正确的定理写出每一步的理由。本文将讲解最重要的定理、常见问题与解题策略。
1. Key Parts of a Circle | 圆的基本要素
Before applying any theorem, you must be able to name the parts of a circle with confidence. The table below summarises the key terms used in circle geometry questions.
在应用任何定理之前，你都必须能够准确说出圆的各个部分的名称。下表总结了圆几何问题中的关键术语。
| Term | 术语 | Definition | 定义 |
| Centre | 圆心 | The fixed point equidistant from every point on the circumference. 到圆周上每一点距离相等的定点。 |
| Radius | 半径 | A line from the centre to a point on the circle. 从圆心到圆上一点的线段。 |
| Diameter | 直径 | A line passing through the centre joining two points on the circle; twice the radius. 过圆心连接圆上两点的线段，是半径的两倍。 |
| Chord | 弦 | A line joining two points on the circle, not necessarily through the centre. 连接圆上两点的线段，不一定过圆心。 |
| Arc | 弧 | A portion of the circumference. 圆周的一部分。 |
| Segment | 弓形 | The region between a chord and the arc it cuts off. 弦与其所截弧之间的区域。 |
| Tangent | 切线 | A line that touches the circle at exactly one point. 与圆恰好只有一个交点的直线。 |
In the diagram shown in your student book, the centre is often labelled O. When writing solutions, always refer to the exact labels, such as OA, OB, AB, or the tangent at T.
在学生用书的图中，圆心通常标为 O。书写解答时，一定要使用准确的字母标记，如 OA、OB、AB 或过点 T 的切线。
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