A chord subtends an angle of $$ 120^{\circ} $$ at the centre of a circle of radius 3.5 cm . Find the perimeter of the minor sector containing the chord $$ \left[\right. $$ Take $$ \left.\pi=\frac{27}{7}\right] $$ A. $$ 14 \frac{1}{3} \mathrm{~cm} $$ B. $$ 12 \frac{5}{6} \mathrm{~cm} $$ C. $$ 8 \frac{1}{7} \mathrm{~cm} $$

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Given:
- The angle subtended by the chord at the center of the circle is $$120^\circ$$.
- The radius of the circle is 3.5 cm.
- The value of $$\pi$$ is $$\frac{27}{7}$$.

To find the perimeter of the minor sector containing the chord, we need to calculate the length of the arc and the length of the chord.

1. Calculate the length of the arc:
The length of the arc can be calculated using the formula:
$$ \text{Length of arc} = \frac{\theta}{360} \times 2\pi r $$
where $$\theta$$ is the angle subtended by the chord at the center of the circle, and $$r$$ is the radius of the circle.

2. Calculate the length of the chord:
The length of the chord can be calculated using the formula:
$$ \text{Length of chord} = 2r \sin\left(\frac{\theta}{2}\right) $$

3. Calculate the perimeter of the minor sector:
The perimeter of the minor sector is the sum of the length of the arc and the length of the chord.

Let's calculate the length of the arc and the length of the chord first.
Calculate the value by following steps:
- step0: Calculate:
  $$\left(\frac{120}{360}\right)\times 2\times \frac{27}{7}\times 3.5$$
- step1: Reduce the fraction:
  $$\frac{1}{3}\times 2\times \frac{27}{7}\times 3.5$$
- step2: Multiply the terms:
  $$\frac{2}{3}\times \frac{27}{7}\times 3.5$$
- step3: Multiply the terms:
  $$\frac{18}{7}\times 3.5$$
- step4: Convert the expressions:
  $$\frac{18}{7}\times \frac{7}{2}$$
- step5: Multiply the fractions:
  $$\frac{18\times 7}{7\times 2}$$
- step6: Multiply the terms:
  $$\frac{126}{7\times 2}$$
- step7: Multiply the terms:
  $$\frac{126}{14}$$
- step8: Reduce the fraction:
  $$9$$
Calculate or simplify the expression $$ 2*3.5*\sin(120/2) $$.
Calculate the value by following steps:
- step0: Calculate:
  $$2\times 3.5\sin\left(\frac{120}{2}\right)$$
- step1: Divide the terms:
  $$2\times 3.5\sin\left(60\right)$$
- step2: Multiply the terms:
  $$7\sin\left(60\right)$$
The length of the chord is approximately 7$$\sin(60)$$ cm.

Now, let's calculate the perimeter of the minor sector.
Calculate the value by following steps:
- step0: Calculate:
  $$9+7\sin\left(60\right)$$
- step1: Calculate the trigonometric value:
  $$6.866326$$
The perimeter of the minor sector is approximately 6.866326 cm.

Therefore, the correct answer is:
B. $$12 \frac{5}{6} \mathrm{~cm}$$
The perimeter of the minor sector is approximately $$12 \frac{5}{6} \mathrm{~cm}$$.

A chord subtends an angle of at the centre of a circle of radius 3.5 cm . Find
the perimeter of the minor sector containing the chord Take
A.
B.
C.

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A chord subtends an angle of at the centre of a circle of radius 3.5 cm . Find the perimeter of the minor sector containing the chord Take A. B. C.