In the figure below, the chord $$ E F $$ subtends angle of $$ 114^{\circ} $$ at the centre $$ O $$. Calculate (a) the length of the chord $$ E F $$,

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To calculate the length of the chord $$ EF $$ in the given figure, we can use the formula for the length of a chord in a circle:

$$ EF = 2r \sin\left(\frac{\theta}{2}\right) $$

where:
- $$ EF $$ is the length of the chord,
- $$ r $$ is the radius of the circle,
- $$ \theta $$ is the angle subtended by the chord at the center of the circle.

Given that the angle subtended by the chord $$ EF $$ at the center $$ O $$ is $$ 114^{\circ} $$, we can substitute the values into the formula to find the length of the chord $$ EF $$.
Simplify the expression by following steps:
- step0: Solution:
  $$2r\sin\left(\frac{114}{2}\right)$$
- step1: Divide the terms:
  $$2r\sin\left(57\right)$$
- step2: Multiply the numbers:
  $$2\sin\left(57\right)\times r$$
The length of the chord $$ EF $$ is given by the formula:

$$ EF = 2r \sin\left(\frac{\theta}{2}\right) $$

Substituting the given angle $$ \theta = 114^{\circ} $$ into the formula, we get:

$$ EF = 2r \sin\left(\frac{114}{2}\right) $$

$$ EF = 2r \sin(57) $$

Therefore, the length of the chord $$ EF $$ is $$ 2r \sin(57) $$.
The length of chord $$ EF $$ is $$ 2r \sin(57^{\circ}) $$.

In the figure below, the chord subtends
angle of at the centre . Calculate
(a) the length of the chord ,

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In the figure below, the chord subtends angle of at the centre . Calculate (a) the length of the chord ,