🎯 Knowledge Check
Maths — AREAS RELATED TO CIRCLES
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Frequently Asked Questions
A circle is the locus of all points in a plane that are at a fixed distance, called the radius, from a fixed point known as the centre.
The area of a circle is the region enclosed by its circumference and is calculated using the formula \(A = \pi r^2\).
\(\pi\) is a constant representing the ratio of the circumference of a circle to its diameter, commonly taken as \(\frac{22}{7}\) or 3.14.
A sector is the region bounded by two radii and the arc between them.
A minor sector is the smaller sector formed when the central angle is less than \(180^\circ\).
A major sector is the larger sector formed when the central angle is greater than \(180^\circ\).
The area of a sector is \(\frac{\theta}{360^\circ} \times \pi r^2\), where \(\theta\) is the central angle.
The angle at the centre determines what fraction of the circle the sector occupies, directly affecting its area.
A segment is the region bounded by a chord of a circle and the corresponding arc.
A minor segment is the smaller region formed between a chord and the corresponding minor arc.
A major segment is the larger region formed between a chord and the corresponding major arc.
Area of minor segment = Area of corresponding sector - Area of the triangle formed by the radii and chord.
Area of major segment = Area of the circle - Area of the minor segment.
A triangle helps remove the straight-line portion inside the sector, leaving only the curved region of the segment.
A chord is a line segment joining any two points on the circumference of a circle.