Circles



We come across many circular objects in our daily life. Let us know about a circle and explore other  related terms. We shall also see some of the properties of a circle.

A circle is the locus of a point equidistant from a fixed point in a plane. In other words, a circle is a collection of all the points in a plane, which are at a fixed distance from a fixed point. The fixed point is called the centre of the circle and the fixed distance is called the radius of the circle.

The line segment joining any two points on a circle is called a chord. The chord which passes through the centre is called a diameter of the circle. The length of a diameter of a circle is twice the length of its radius.

A piece of a cirlce between two points is called an arc of the circle. The shorter arc is called the minor arc and the longer one is called the major arc.

A diameter divides a circle into two semi circles.

The length of the complete circle is called its circumference.

A circle divides a plane into two parts. One is the interior and the other is the exterior. A circle together with its interior is called the circular region.

A diameter divides the circular region into two semi circular regions.

The part of the circular region bounded by two radii and the corresponding arc is called a sector. The smaller one is called the minor sector and the larger one is called the major sector.

A chord divides a circular region into two segments. The smaller one is called the minor segment and the larger one is called the major segment.

Can a segment be a sector? Yes! A semicircular region is a segment which is also a sector.

The angle subtended by an arc at the centre is called the central angle. The central angle of an arc is twice the angle subtended it in the alternate segment.

A quadrilateral whose vertices lie on a circle is called a cyclic quadrilateral. Opposite angles of a cyclic quadrilateral are supplementary.

Equal chords of a circle are equidistant from the centre of the circle. Equidistant chords of a circle from its centre are equal in length.

Are you ready for a quiz?

Choose the correct option from the brackets to fill up the blanks.

1. A line segment joining the centre to a point on the circle is called __________ (radius/diameter)

2. A line segment joining two points on a circle is a_______(chord/ diameter)

3. The centre of a circle is in the _________ (interior/exterior)

4. The longest chord of a circle is ________(radius/diameter)

5. Diameter is  _____________( half the radius/double the radius)

6. A piece of a circle between two points  on the circle is  ______(chord/arc)

7. The shorter arc of a circle is called _______ (minor arc/major arc)

8. The length of the complete circle is called its _______ ( area/circumference)

9. The region between a chord and its arc is called______( sector/segment)

10. The region between two radii and the corresponding arc is called a ________(sector/segment)

Hope you enjoyed this simple lesson on circles.

 

 

 

 

 

 

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