Question

Class 10

Mathematics

Chapter 12 - Area realted to Circles
Formulas Needed

Quality Answer Needed​

Answer 1

Step-by-step explanation:

Circle :-

The set of all points from a fixed point to fixed distance in a plane is called a circle. The fixed point is called its centre and the fixed points is called its radius .

Radius is denoted by 'r'.

Parts:-

• Circumference:-

The total length of the circle is called its circumference and it is denoted by C.

• The radius of the circle is 'r' units then the circumference of the circle is "2πr" units .Where π=22/7.
• The circumference of a circle (C) when diameter (d) is given πd units
• Area of a circle when radius (r) is given is πr^2 sq.units
• Area of a circle when the diameter (d) is given πd^2/4 sq.units
• Area of a circle when the circumference(C) is given C^2/4π sq.units

Chord:-

• The line segment joining any two points on the circumference of the circle is called its a chord .
• We can draw so many chords to the circle.
• The longest of all chords of a circle is its diameter and it is denoted by 'd'.
• d=2r units

Arc:-

• The part of a Circumference of the circle is its arc.

Sector :-

The area enclosed by two radii and the arc is called the sector of the circle.

• Radius of a circle is 'r' units and the angle subtended by an arc at the centre is X° then area of a sector = (X°/360°)×πr^2 sq.units

• Length of the arc =( X°/360°)×2πr sq.units

• Area of a sector when length of the arc(l) and radius (r) are given is A= lr/2 sq.units

• Length of the arc when radius(r) and area of the sector (A) are given is l=2A/r units

segment:-

Area enclosed by a chord and an arc is called is a segment.

• If an arc is minor then it is a minor segment.

• If an arc is major then it is a major segment.

• Area of a segment = Area of a sector - Area of a the corresponding triangle in the sector.

• Area of a segment =[(X°×πr^2)/360°] - [(r^2 SinX°)/2 ]

• Area of a minor segment = Area of a circle - area of a major segment.

• Area of a major segment = Area of a circle - Area of a minor segment .