Exercise 6G: Circles and Triangles | 练习6G：圆与三角形

📚 Exercise 6G: Circles and Triangles | 练习6G：圆与三角形

Exercise 6G brings together everything you have learned about circles: the equation of a circle, perpendicular bisectors, and solving simultaneous equations. In this lesson you will find the equation of a circle that passes through three given points – the circumcircle of a triangle. This is a favourite AQA exam question, worth significant marks, and it tests your algebraic fluency as well as your geometric insight.

练习6G将你学过的关于圆的所有知识整合在一起：圆的标准方程、垂直平分线以及联立方程的求解。在本课中，你将学会求经过三个已知点的圆的方程——即三角形的外接圆。这是AQA考试中的高频题型，分值较高，既考查代数运算能力，也考查几何直观。

1. The Circle Equation | 圆的标准方程

Recall the equation of a circle with centre (a, b) and radius r. This is the centre-radius form, and it is the starting point for every problem in Exercise 6G.

回顾圆心为 (a, b)、半径为 r 的圆的标准方程。这是本练习所有题目的出发点。

(x – a)² + (y – b)² = r²

Expanding the brackets gives the general form x² + y² + Dx + Ey + F = 0, where D = -2a, E = -2b and

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