# Parts of Circle

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**Relation between diameter and radius**

Diameter = 2 x radius

Or radius = r = d / 2.

**Circumference ( C ) :**The length of a boundary of a circle.

C = 2 Πr

Or C = Π D

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**Examples**

1) Radius = 4 cm, find the diameter.

**Solution :**

Diameter = 2 x radius

⇒ Diameter = 2 x 4

⇒ Diameter = 8 cm.

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2) Diameter = 6.4 cm, find the radius.

**Solution :**

radius = r = d / 2.

⇒ radius = 6.4/2

⇒ radius = 3.2 cm

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2)If the radius of circle is 1.5 cm then find the diameter and the circumference.

**Solution :**

Diameter = D = 2 r

D = 2 x 1.5

D = 3 cm.

Circumference = C = &pie;D

C = 3.14 x 3

C = 9.42 cm

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Some more parts of circle are as follows:

**Arc :**A part of a circle between any two points on the circle.

There are two types of arcs 1) Minor arc 2) Major arc.

Here PQR is the minor arc and PR is a major arc.

As arc is a part of a circle so,

**Length of a minor arc = Π rθ / 180**

Length of major arc = 2Πr - Π rθ / 180

Length of major arc = 2Πr - Π rθ / 180

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**Examples**

1) Find the length of arc of radius 6 cm and angle formed by the two radii is 60

^{0}.

**Solution :**

r = 6 cm , θ = 60

^{0}and Π = 3.14

Length of a minor arc = Π rθ / 180

Length of a minor arc = ( 3.14 x 6 x 60 ) / 180

Length of arc = 6.28 cm

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2)

**Sector :**The region enclosed by two radii and an arc.

Area ( minor sector ) = Πr

^{2}θ / 360

Area ( major sector) = Πr

^{2}- Πr

^{2}θ / 360

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**Example :**Find the area of sector whose radius is 8 cm , angle θ 30

^{0}and Π = 3.14.

**Solution :**

r = 8 cm , θ = 30

^{0}and Π = 3.14

Area of sector = Πr

^{2}θ / 360

Area = (3.14 x 8

^{2}x 30 ) / 360

Area of sector = 16.75 cm

^{2}

**Circles**

• Circles

• Parts of Circle

• Arc and Chords

• Equal Chords of a Circle

• Arc and Angles

• Cyclic Quadrilaterals

• Tangent to Circle

• Circles

• Parts of Circle

• Arc and Chords

• Equal Chords of a Circle

• Arc and Angles

• Cyclic Quadrilaterals

• Tangent to Circle

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