Subject: Compulsory Maths

A circle is a plane figure bounded by a curved line and every point of the line is equidistance from a fixed point called the centre of the circle.

**Circumference of circle**

The curved boundary line of a circle sis called its circumstance. The length of the circumference represents the perimeter of the circle.**Radius of a circle**

The straight line is drawn from the centre of a circle to a point on its circumference is called the radius of the circle.

In the given figure, OA is the radius.**Chord of a circle**

The straight line segment that joins any two points on the circumference of a circle is called the chords of a circle.

In the given figure, AB is the chord of the circle.**Diameter of a circle**

The chord that passes through the centre of a circle is called the diameter of the circle. Diameter is also called the largest chord of any circle. In the given figure, CD is the diameter of a circle. The length of the diameter of a circle is two times its radius.

\(\therefore\) Diameter = 2 × radius**Sector of a circle**

The region inside a circle bounded by its two radii (plural of radius is radii) is called sector.

In the figure, the shaded region AOB is the sector.**Arc of a circle**

The part of a curve between two given points on the curve of a circle is called an arc.

In the figure, AB is the arc.**Segment of a circle**

The region bounded by an arc and its corresponding chord is called the segment of a circle.

In the given figure, the shaded region represents a segment.**Semi-circle**

Half part of a circle is called a semi-circle. A diameter divides a circle into two halves and each half is the semi-circle.

In the given figure, ABC is a semi-circle.

- The length of the circumference represents the perimeter of the circle.
- The length of the diameter of a circle is two times its radius.
- Half part of a circle is called a semi-circle.

- It includes every relationship which established among the people.
- There can be more than one community in a society. Community smaller than society.
- It is a network of social relationships which cannot see or touched.
- common interests and common objectives are not necessary for society.

Define circle.

A circle is a plane figure bounded by a curved line and every point of the line is equidistance from a fixed point called centre of the circle.

Mention the different parts of a circle.

The different parts of a circle are:

- Circumference of a circle
- Radius of a circle
- Chord of a circle
- Diameter of a circle
- Sector of a circle
- Arc of a circle
- Segment of a circle
- Semi-circle

Draw the following figures and find out the centre:

Figure (a)

Figure (b)

Figure(c)

Solution:

Centre of figure a) = O

Centre of figure b) = P

Centre of figure c) = A

Find the radii, chords, diameters, sectors, arcs, segments and semi-circles from following figures:

Figure (a)

Figure (b)

Figure (c)

Solution:

Figure a) = radii OA and OB, sector OAXB and arc AXB

Figure b) = segment CDY and Chord CD

Figure c) = semi-circle MYN and MXN, diameter MN

Copy the figures and find the opposite arc of each angle:

Figure (a)

Figure (b)

Figure (c)

Figure (d)

Solution:

Angle | Opposite Arc |

\(\angle\)ABC | AXC |

\(\angle\)PQR | PYR |

\(\angle\)KLM, \(\angle\)KNM, \(\angle\)LKN, \(\angle\)LMN | KPM, LN |

\(\angle\)ABC, \(\angle\)ADC, \(\angle\)BAD, \(\angle\)BCD | AEC, BD |

Copy the figures and find the centre and radii. Also find the arc opposite to each angle.

Figure (a)

Figure (b)

Figure (c)

Figure (d)

Figure (e)

Figure (f)

Figure (g)

Figure (h)

Solution:

Centre and Radii of figure a) = OA and OB

Centre and Radii of figure b) = CP and DP

Centre and Radii of figure c) = EQ and FQ

Centre and Radii of figure d) = KM and KN

Angle | Opposite Arc |

\(\angle\)AOB | AXB |

\(\angle\)CPD | CYD |

\(\angle\)EQF | EZF |

\(\angle\)MKN | MSN |

What is the difference between the radius and diameter of a circle?

The straight line drawn from the centre of a circle to a point on its circumference is called the radius of a circle whereas the chord that passes through the centre of a circle is called the diameter of a circle.

What is the difference between the chord and segment of a circle?

The straight line segment that joins any two points on the circumference of a circle is called the chord of a circle. However, The region bounded by an arc and its corresponding chord is called the segment of a circle.

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