Hello friends,Previously we have discussed about operations with rational numbers and today we are going to learn about Properties of circles, circle for grade VI of karnataka board. Before, we move to the topic, it necessary to know about the circle that can provide you help with math in solving problems. In geometry circle is a simple shape and defined as the set of points that are equally distance from the centre of the circle or its origin. a line whose endpoints lie on the circle and passes through the centre of circle is called diameter and this line has largest distance between any two points on the circle. A line that intersects the circle or a curve at two points is called secant. Radius is a line which is half of the diameter. Now area of the circle is defined as total space inside the boundary of the circle. The area of a circle can be found if the radius of the circle is given with the help of formula that is,(for more help with circle refer this)
Area=r2 where r is the radius of circle and is an irrational constant and approximately equal to 3.141592654.
If we have the value of diameter (d) and radius than circumference of circle is
C=2r=d, where d is diameter
Lets we are discussing about the Properties of circles. In geometry, the properties of the circle consist of large number of facts about circles and their relations to straight lines, angles and polygons. All Properties of circles are given below.
Circles having equal radius are congruent and having different radius are similar.
The circle's radius and circumference are proportional and circle having the largest area for a given length of perimeter.
The square of radius and the area enclosed are proportional and constants of proportionality are 2π and π.
A circle which has radius 1 at its centre of origin is called the unit circle.
A radius perpendicular to a chord bisects the chord and chords is one which is equidistant from the center are equal in length. The longest chord of the circle is diameter and equal chords have equal circumferences.
If any two chords intersect and divides one chord into lengths p and q and divides the other chord into lengths r and s, then pq = rs. On other hand if any two perpendicular chords intersect and divides one chord into lengths p and q then p2+q2+r2+s2 equals the square of the diameter.
A tangent to a circle is the line perpendicular drawn to a radius through the end point of the radius.
If two tangents drawn from a point outside to a circle then they are equal in length.
The angle subtended at the origin by its circumference is equal to four right angles. The circumference of two different circles is proportional to their corresponding radii and the arcs (The connected part of the circle's circumference is called arc) of the same circle are proportional to their corresponding angles of that circle.
The equal circles or radii of the same circle are equal. These are the Properties of circles.
From the above discussion I hope that it would be helpful for you to understand Properties of circles and if anyone want to know about Evaluating formulas
then they can refer to internet and text books for understanding it more precisely. You can also refer Grade VII blog for further reading on Properties of lines.
Area=r2 where r is the radius of circle and is an irrational constant and approximately equal to 3.141592654.
If we have the value of diameter (d) and radius than circumference of circle is
C=2r=d, where d is diameter
Lets we are discussing about the Properties of circles. In geometry, the properties of the circle consist of large number of facts about circles and their relations to straight lines, angles and polygons. All Properties of circles are given below.
Circles having equal radius are congruent and having different radius are similar.
The circle's radius and circumference are proportional and circle having the largest area for a given length of perimeter.
The square of radius and the area enclosed are proportional and constants of proportionality are 2π and π.
A circle which has radius 1 at its centre of origin is called the unit circle.
A radius perpendicular to a chord bisects the chord and chords is one which is equidistant from the center are equal in length. The longest chord of the circle is diameter and equal chords have equal circumferences.
If any two chords intersect and divides one chord into lengths p and q and divides the other chord into lengths r and s, then pq = rs. On other hand if any two perpendicular chords intersect and divides one chord into lengths p and q then p2+q2+r2+s2 equals the square of the diameter.
A tangent to a circle is the line perpendicular drawn to a radius through the end point of the radius.
If two tangents drawn from a point outside to a circle then they are equal in length.
The angle subtended at the origin by its circumference is equal to four right angles. The circumference of two different circles is proportional to their corresponding radii and the arcs (The connected part of the circle's circumference is called arc) of the same circle are proportional to their corresponding angles of that circle.
The equal circles or radii of the same circle are equal. These are the Properties of circles.
From the above discussion I hope that it would be helpful for you to understand Properties of circles and if anyone want to know about Evaluating formulas
then they can refer to internet and text books for understanding it more precisely. You can also refer Grade VII blog for further reading on Properties of lines.
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