IGCSE Maths: Circle Theorems | IGCSE 数学：圆定理

📚 IGCSE Maths: Circle Theorems | IGCSE 数学：圆定理

Circle theorems are a central part of IGCSE Mathematics. They describe angle and length relationships within circles, and they appear frequently in both core and extended papers. This article covers the key theorems, worked examples, and exam strategies linked to Student Book G-3 page 200.

圆定理是 IGCSE 数学的核心内容。它们描述了圆内角与线段之间的关系，在核心卷和扩展卷中都很常见。本文结合学生用书 G-3 第200页的内容，讲解关键定理、例题和考试策略。

1. Circle Terminology | 圆的基本术语

Before using circle theorems, you need to recognise the main parts of a circle. The centre O is the point from which all points on the circumference are the same distance r.

在使用圆定理之前，你需要识别圆的主要部分。圆心 O 是到圆周上所有点距离都等于半径 r 的点。

A chord is a segment joining two points on the circle, an arc is a portion of the circumference, and a tangent is a line that touches the circle at exactly one point without crossing it.

弦是连接圆上两点的线段，弧是圆周的一部分，切线是与圆恰好相交于一点且不穿过圆的直线。

In IGCSE diagrams, the radius is often drawn to a tangent or to the midpoint of a chord, so always mark these equal distances and right angles clearly.

在 IGCSE 图形中，半径经常画到切线或弦的中点，因此务必清楚标出这些相等的距离和直角。

r = d ÷ 2 and d = 2r

2. Angle at the Centre Theorem | 圆心角定理

This is the most important circle theorem: the angle at the centre is twice the angle at the circumference when both angles are subtended by the same arc.

这是最重要的圆定理：当圆心角和圆周角由同一段弧所对时，圆心角等于圆周角的两倍。

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