Lines and circles are the important elementary numbers in geometry. We recognize that a heat is a locus of a allude moving in a consistent direction, whereas the one is a locus of a suggest moving in ~ a constant distance indigenous some solved point. The theoretical prestige of the one is reflect in the number of amazing applications. Below we will comment on the properties of a circle, area and circumference that a circle in detail.

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Circle Definition

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The repertoire of all the clues in a plane, which are at a solved distance native a fixed suggest in the plane, is called a circle. Here, the fixed allude is called the centre “O”. Several of the vital terminologies offered in the circle space as follows:

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Terms Description
CircumferenceThe border of the one is recognized as the circumference
RadiusThe line from the centre “O” of the circle to the one of the circle is dubbed the radius and also it is denoted through “R” or “r”
DiameterThe line the passes with the centre of the circle and also touches the two points on the circumference is called the diameter andit is denoted by the price “D” or “d”
ArcArc is the component of the circumference where the largest arc is dubbed the major arc and also the smaller one is referred to as the minor arc
SectorSector is part of a one bounded by two radii and also the consisted of arc the a circle
ChordThe straight line the joins any kind of two clues on the circumference of a circle is dubbed the chord
TangentA line that touches the circumference of a circle in ~ a point is referred to as the tangent
SecantA line that cut the circle in ~ the two distinctive points is known as the secant

Circle Properties

Some that the crucial properties that the circle room as follows:

The one are claimed to it is in congruent if they have actually equal radiiThe diameter that a one is the longest chord of a circleEqual chords the a one subtend equal angles at the centreThe radius attracted perpendicular to the chord bisects the chordCircles having different radius are similarA circle can circumscribe a rectangle, trapezium, triangle, square, kiteA circle can be inscribed inside a square, triangle and also kiteThe chords that are equidistant indigenous the centre are equal in lengthThe distance from the centre of the circle come the longest chord (diameter) is zeroThe perpendicular street from the centre of the circle decreases when the length of the chord increasesIf the tangents are attracted at the end of the diameter, they are parallel to every otherAn isosceles triangle is created when the radii authorized the end of a chord to the centre of a circle

Circle Formulas

Area that a circle, A = πr2 square units

The circumference of a one = 2πr units

The one of a one formula can additionally be created as πd.

Where,

Diameter = 2 x Radius

d = 2r

Here “r” to represent the radius the a circle.

Circle Problem

The sample instance to find the area and also circumference of a circle is provided below.

Question:

Find the area and circumference of a circle having actually the diameter value of 10 cm.

Solution:

Given:

Diameter, d = 10 cm

We recognize that diameter = 2 x Radius

Therefore, radius, r = d/2

r = 10/2 = 5

So, the radius is 5 cm.

Area the a circle, A = πr2 square units

A = 3.14 x 5 x 5

Where ,

π = 3.14

A = 3.14 x 25

A = 78.5 cm2

Therefore, the area that a circle is 78.5 square units

The one of a one = 2πr units

C = 2 x 3.14 x 5

C = 10 x 3.14

C = 31. 4 cm

Therefore, the circumference of a circle is 31.4 units.

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