Circles in Grade VI

Hello friends, in today' session we are going to learn about a very interesting topic of Geometry (brief definition taken from syllabus for class 9th ICSE), Circles. So let's just start by understanding its definition.
A circle is defined as a simple shape which consists of those points in a plane which are at a given distance from a given point. The given point is called as the center and the given distance is called the radius. The radius could also be understood as the distance from the center to the circumference of the circle.
Another more simple definition of circle could be the curve formed by a point that moves so that its distance from a given point is always constant.
The terminology of the circle includes the following -
Diameter – it is the length of the line segment whose end points lie on the circle and it passes through the center. The diameter of the circle divides it into two equal halves.
Radius – the half of the diameter of the circle is called the radius.
Chord – the line segment whose end points lie on the circle.
Tangent – it is a straight line which touches the outside of the circle at a single point.
Arc – it is any part of the circumference of the circle.
Sector – it is a region bounded by the two radii of the circle.
Segment- it is the region bounded by the chord and the arc of a circle.
The radius of the circle in general is represented as r and the diameter as d.
The circumference of the circle is given by the formula C = 2 π r.
and the area is given by A = π r ².
Now you have got the basic knowledge on what circle is and how to find its area and circumference.
So let's now move towards the properties of the circle. The properties will help you a lot in solving the problems on circles.

1. 
   
   1. Circles with equal radii are always congruent.
   2. Circles which have a different radii are similar.
   3. The central angle which intercepts an arc is double of any inscribed angle that intercepts the same arc.
   4. If the radius is perpendicular to the chord then it will bisect the chord i.e. divide it into two equal halves.
   5. If the distance of the chord is equal from the center then the chords are also equal in length.
   6. The tangent of the circle is always at right angle to the radius at the point of contact.
   7. Two tangents drawn to the circle from the exterior are always equal in length.
   8. The angle subtended at the center of the circle by its circumference is equal to 360⁰.
   9. Circumference of two circles of different radii is proportional to their corresponding radii.
   10. Arcs formed by the same circle are proportional to their corresponding radii.
   11. Radii of the circle is always constant.
   12. If the chords of a circle are equal in length then they have equal circumference.
   13. The diameter of the circle is its longest chord.
   14. If the radii of two circles are equal then the circles are equal.
   15. If the circles are equal then their circumference is also equal.
       
       In next post we will talk on Similar Triangles in Grade VI. For more information on math word problems, you can visit our website