By How can You Find the Area of the Major Segment Using the Minor Segment?
Simple put it can be done by the formula:
Major Segment = Area of the Circle – Area of Minor Segment.
What is a circular segment- This is a Circle sector or disk sector. This is a portion of a disk which is a closely bounded area by a circle and is enclosed by radii and an arc and here the smallest area is the one known as the Minor Sector and the larger sector known as Major Sector.
Thus the angle formed by the connection of the endpoints of the Arc to any point in the circumference that is not in the sector is equal to half the central angle.
MINOR SECTOR: Sector which is less than a semi circle.
MAJOR SECTOR: This sector is greater than semi-circle.
Applications for them- When we calculate the area for any space , then this formula is used to calculate the volume of any cylinder space laying in a horizontal position. In some designs for home windows and door with tops where it is round in shape, There are some values and you can use it to calculate the compass setting. One can also calculate the full dimension for a complete circle by calculating the arc measurements and other elements in the arc of the circle. Sometimes to check the hole positions for any position of circular parameter and pattern. This is useful for checking the machine products. We can also use this for calculation of any area or centroid for any shape containing the circular segments.
The circle is known to have the following properties:
- The shape with the largest area for any given length of perimeter.
- This is highly symmetrical and thus every line that passes through the centre forms a line of reflection and is thus also symmetrical. It has symmetry which is rotational around the centre of each angle. The symmetry group is the orthogonal group. All the circle are similar in properties.
- In the circle the circumference and radius is always equal and in proportion. The radius and its area which is enclosed by the circle is also proportional.
- The circle which is centred at the origin is the unit circle. Through any given three points n the circle, but not necessarily on the same line it is possible to give formulas for the centre coordinates and the radius of the circle in terms of co-ordinates of the given points which we initially took.
What is a chord: This is the space which is equidistant from the centre of the circle. The condition is that they are to be equal in size. There is a perpendicular bisector of the chord which when passes through the circle centre. When there is a perpendicular line it goes from the centre of the circle and it bisects the chord. The line segment through the centre of the chord is in perpendicular position to the chord. If we have one central angle and an another one angle for a circle which is increased then it is subtended by the same chord and thus it will be on the same side of the chord.
Here the central angle is twice the angle which is inscribed. Thus two angles which are inscribed on the same chord and also on the same side then they are equal. However if the two angles are inscribed on different sides of the chord then they are called supplementary. For any cyclic quadrilateral the external angle is same to the opposite angle which is inside the circle. However the inscribed angle which is extended by the diameter is the right angle. The angle which is inscribed is the right angle and is actually extended by the diameter.
Learn More: Areas Related to Circles from Class 10 Maths
Tangent of a circle: This is the line which is drawn to the circle radius and is perpendicular to it and thus lie on the end point of the radius on the circle. This is called the Tangent of the circle.This is perpendicular to the tangent and through its point of contact it passes by the circle centre. Two of the tangents of the circle can always be drawn to a circle from any point outside of the circle space and thus these tangents are always equal in length and size.