Edexcel IGCSE Maths 复习笔记 4.6.3 Circle Theorems - Cyclic Quadrilaterals

Edexcel IGCSE Maths 复习笔记 4.6.3 Circle Theorems - Cyclic Quadrilaterals

More advanced circle theorems

1. Opposite angles in a cyclic quadrilateral add up to 180°

Cyclic-quadrilaterals

 

  • Double-check is that all 4 vertices of the quadrilateral are on the circumference
  • The diagram below shows a common scenario that is NOT a cyclic quadrilateral:

 

Not-cyclic-quad-point-at-centre 

2. The perpendicular bisector of a chord is a radiusRadius-chord-bisect

  • This is also easier to see than remember from its description
  • Problems here involve the radii being joined to the end of the chords and so creating two congruent triangles

 

Exam Tip

Remember to add anything you can to a diagram you have been given – write in any angles and lengths you can work out, even if they don’t seem relevant to the actual question.

Worked Example

7.16.3-Circle-Theorems-Cyclic-Quadrilaterals-Worked-Example-1Q1-Circle-Theorems-37.16.3-Circle-Theorems-Cyclic-Quadrilaterals-Worked-Example-2

Worked Example

Q1-CT3-Working-in-red7.16.3-Circle-Theorems-Cyclic-Quadrilaterals-Worked-Example-3

转载自savemyexam

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