Question

In the figure the length of the arc CNB is 1/5 of the perimetre of the circle and the length of the arc AMD is 1/6 of the perimetre of the circle. (a) What is the measure of centre angle of the arc CNB ?

Answer 1

Given :-

• The length of the arc CNB is 1/5 of the perimetre of the circle.
• The length of the arc AMD is 1/6 of the perimetre of the circle.

To Find :-

• a) What is the measure of centre angle of the arc CNB ?
• b) What is the measure of centre angle of the arc AMD ?

Solution :-

we know that, Length of arc is directly Proportional to angles subtends at the centre.

So,

• (The length of arc / circumference of circle) = (Angle at centre / 360°)

we have given that,

→ The length of the arc CNB = 1/5 of the perimetre of the circle.

Than,

→ (The length of the arc CNB / perimetre of the circle) = 1/5

Therefore,

→ (1/5) = (Angle at centre / 360°)

→ 5 * Angle at centre = 360°

Dividing both sides by 5,

→ Angle at centre = 72° (Ans.)

Hence, centre angle of the arc CNB is 72° .

___________________

Similarly,

→ The length of the arc AMD = 1/6 of the perimetre of the circle.

Than,

→ (The length of the arc AMD / perimetre of the circle) = 1/6

Therefore,

→ (1/6) = (Angle at centre / 360°)

→ 6 * Angle at centre = 360°

Dividing both sides by 6,

→ Angle at centre = 60° (Ans.)

Hence, centre angle of the arc AMD is 60° .

_________________________