**Circumference of a Circle or Perimeter of a Circle**

- The distance around the circle or the length of a circle is called its circumference or perimeter.
- Circumference (perimeter) of a circle = πd or 2πr,

where d is a diameter and r is a radius of the circle and π = - Area of a circle = πr
^{2} - Area of a semicircle = πr
^{2} - Area of quadrant = πr
^{2}

**Perimeter of a semicircle:**

Perimeter of a semicircle or protractor = πr + 2r

**Area of the ring Formulas :**

Area of the ring or an annulus = πR^{2} – πr^{2}

= π(R^{2} – r^{2})

= π (R + r) (R – r)

Length of the arc AB = =

**Area of sector formula:**

- Area of sector OACBO =
- Area of sector OACBO = (r × l).

**Perimeter of a sector Formula:**

Perimeter of sector OACBO = Length of arc AB + 2r

= + 2r

Other important formulae:

- Distance moved by a wheel in 1 revolution = Circumference of the wheel.
- Number of revolutions in one minute =
- Angle described by minute hand in 60 minutes = 360°
- Angle described by hour hand in 12 hours = 360°
- The mid-point of the hypotenuse of a right triangle is equidistant from the vertices of the triangle.
- The angle subtended at the circumference by a diameter is always a right angle.

**Area of a segment Formula Class 10 :**

- Area of minor segment ACBA = Area of sector OACBO – Area of ΔOAB

= - Area of major segment BDAB = Area of the circle – Area of minor segment АСВА

= πr^{2}– Area of minor segment ACBA. - If a chord subtends a right angle at the centre, then

Area of the corresponding segment = - If a chord subtends an angle of 60° at the centre, then

Area of the corresponding segment = - If a chord subtends an angle of 120° at the centre, then

Area of the corresponding segment =