Key Points - Area Related to Circles

- Circle: A circle is the locus of a point which moves in a plane in such a way that its distance from a fixed point always remains the same. The fixed point is called the center and given constant distance is known as the radius of the circle.

- Segment of a Circle: The portion (or part) of a circular region enclosed between a chord and the corresponding arc is called a segment of the circle. In adjacent fig. APB is minor segment and AQB is major segment.

- Sector of a Circle: The portion (or part) of the circular region enclosed by the two radii and the corresponding arc is called a sector of the circle. In adjacent figure OAPB is minor sector and OAQB is the major sector.

- Area of circle = πr^2 where ‘r’ is the radius of the circle.

- Area of Semi circle = πr^2 / 2

- Area enclosed by two concentric circles  = π(R^2 − r^2 )
= π(R + r)(R − r); R > r

where ‘R’ and ‘r’ are radii of two concentric circles.

- The arc length ‘l’ of a sector of angle ' θ ' in a circle of radius ‘r’ is given by
 l= θ / 360o × 2πr

 l= θ / 180o × 2πr

- If the arc subtends an angle θ , then area of the corresponding sector is θ / 360o × πr^2 o

- Angle described by minute hand in 60 minutes = 360°. Angle described by minute hand in 1
(360° / 60) = 6°