Circle In Degree & Radian
In this lesson, you will learn how angles in a circle can be measured using both degrees and radians. You will understand that a full circle is 360° or 2π radians, and learn how to convert between these two units.
Related Lessons:
Convert Between Degree & Radian
When converting between degree and radian, we will use the following relationship:
- \(\pi\ rad=180^\circ\)
- \(2\pi\ rad=360^\circ\)
Arc Length & Area Formula For Circle
For circle formula in degree:
- \(arc\ length=\frac{x^\circ}{360^\circ}\times2\pi r\)
- \(sector\ area=\frac{x^\circ}{360^\circ}\times\pi r^2\)
For circle formula in radian:
- \(arc\ length=r\theta\)
- \(sector\ area=\frac{1}{2}r^2\theta\)
Example 1
The diagram shows a major segment of a circle centre O, radius 10 cm. The chord AB is of length 12cm. Calculate
- the perimeter of the segment
- the area of the segment
Example 2
The diagram shows a circle of radius 6cm with centre O. Angle AOB subtended by the arc APB is 80°. A sector CAQB with centre at C is drawn in the circle such that C, A and B lie on the circumference of the circle, and AC=BC.
- Giving your reason, write down ∠ACB
- Show that the length of CA is 11.276cm, correct to 5 significant figures.
- Find the perimeter of the shaded region.
- Find the area of the shaded region.
Example 3
The diagram shows a circle, centre O, of radius 8 cm. The line RP is a tangent to the circle at P and the line OR intersects the circle at Q. Given that ∠ORP is 0.6 radians, calculate
- angle POR, in terms of π,
- the length of the minor arc PQ correct to 1 decimal place.
Example 4
The diagram shows two concentric circles, centre A, of radius r cm and 10 cm. The tangent to the smaller circle B meets the larger circle at D. ABC and AED are straight lines. Given that ∠ BAD = 1.2 radians, calculate
- the value of r
- the length of the minor arc CD
- the area of the shaded region