Chord Of A Circle- GCSE Maths - Steps, Examples & Worksheet

Home » What Are Chords In Geometry » Chord Of A Circle- GCSE Maths - Steps, Examples & Worksheet

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Example 1: cosine ratio

Below is a circle with centre C . Points A, B, C, and D are on the circumference of the circle. The chord AB is perpendicular to the line CD at the point E . The line AE is 5cm and angle ADE = 71° . Calculate the length of the line BC correct to 1 decimal place.

  1. Locate the key parts of the circle for an appropriate circle theorem.

Here we have:

  • CD is a diameter
  • AB is a chord, perpendicular to CD
  • The angle ADE = 71°
  • The angle BEC = 90°
  • The line AE = 5cm
  • The line BC = x

2Use other angle facts to determine other necessary angles.

As angles in the same segment are equal, angle ADE is equal to angle ABC so angle ABC = 71° . Also, as the perpendicular from the centre of a circle to a chord bisects the chord, the line BE is equal to AE , so BE = 5cm .

3Use Pythagoras’ theorem or trigonometry to find the missing length.

To calculate the length of the chord BC , we need to use trigonometry as we know one side length and two angles where one angle is 90° .

As we know the side adjacent to the angle and we want to calculate the hypotenuse, we need to use \cos(\theta)=\frac{A}{H} with H as the subject.

H=\frac{A}{\cos(\theta)}

x=\frac{5}{\cos(71)}

x=15.4cm (1dp)

Tag » What Are Chords In Geometry