How to Draw a Circle of Radius 2.25 Cm

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Radius of a Circle

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The radius of a circumvolve is ordinarily measured from the centre of whatever spherical object to a particular point on the circumference (the edge of the circular object). Radius, every bit is mentioned prior, is signified with the letter of the alphabet "r".

Interestingly, a radius is not simply half the diameter of a circular object, but too for semi-round objects, cones that accept circular bases or even cylindrical objects. Many define a circle as the locus point that typically moves in a aeroplane, particularly such that the measure out remains abiding from the eye to the circumference either way.

In definition, the fixed heart point in equal distance from the circumference, in a mode that every plane remains in parity is known as radius. Nearly circle related formulas, like circumference and area, are adamant by and large past first considering the radius.

Radius of a Circle

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Formula Related to Radius

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1. Radius From Diameter

Diameter of a circumvolve is a plane that passes through the center point and somewhen joins whatsoever betoken by the other finish of the circle. In elementary words, a diameter is twice the distance of a radius. A double radius can give rising to a total diameter. Dominantly, it is the largest chord ever determined and institute in a circle. The formula of diameter is usually signified by:

Diameter = 2r (where, r is the radius)

two. Radius from Circumference

The circumference of a circle is the full length of the circumvolve boundary, usually also defined every bit its perimeter. Mathematically, the circumference of a circumvolve is one of the vital parts that decides many dissimilar areas of a spherical object. The formula of the circumference, in reference to radius, can be given as,

Circumference = 2πr units

 where, r is radius, and π is a abiding, often otherwise expressed as 3.141.

three. Radius from Area

The area of a circle is commonly the total infinite it has occupied. The relationship between area and radius of a circumvolve can gradually be established by the formula:

Area = πr² foursquare units (where, r is the radius).

4. Cartesian Airplane

The radius of a circle can be besides determined through the cartesian aeroplane. By cartesian plane, the following formula tin be obtained: (ten-h)² + (y-1000)² = rⁱⁱ

Read More: Conic Sections

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Chord of a Circle

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The chord of a circle can be divers every bit a straight line segment that has endpoints lying over a given circular arc. In a nutshell, the seemingly infinite line segment of a chord, present in a circle, is known as a secant line. In bulk, there are two formulae that aid measure the chord length of a circle. The formulae are as expressed beneath,

Chord Length = 2 √(r² – d²), this formula is generally used during the adding of a perpendicular drawn out from the middle signal.

While, if speaking trigonometrically, the chord length can exist expressed as = two r sin (c / 2).

Likewise, in reference to both area, diameter and circumference, the following formulae can be adamant:

• Radius = C/2π (for circumference)
• Radius = √(A/π) (for area)
• Radius = D/2 (for diameter)

Chord of a Circle Theorem

Theorem 1: The chord is bisected by a perpendicular line drawn from the center of a circle to information technology.

Given: AB= Chord and OC⊥AB

To prove: Air conditioning=BC

Structure: Draw OA and OB

Proof: In ΔOAC and ΔOBC

Statement	Reason
OA = OB	Radii of the same circumvolve
OC = OC	Common
∠OCA = ∠OCB	xc degree Angle
ΔOAC ≅ ΔOBC	Past RHS congruence rule
Air-conditioning = CB	Past CPCT (Respective parts of coinciding triangles)

Theorem two: The line fatigued through the centre of the circle to bisect a chord is perpendicular to the chord.

Given: The circle'southward chord AB has its midpoint at C, with the circle's centre at O.

To prove: OC⊥AB

Construction: Bring together OA, OB and OC

Proof: In ΔOAC and ΔOBC

S. no	Argument	Reason
1	OA = OB	Radii of the same circumvolve
2	OC = OC	Common
3	∠OCA = ∠OCB	Corresponding parts of congruent triangle
four	∠OCA + ∠OCB = 180 caste	Linear pair angle
5	ΔOAC ≅ ΔOBC	By SSS congruence rule
six	AC = CB	Given
7	∠OCA = ∠OCB = xc degree	From argument 3 and 4
viii	OC ⊥ AB	From argument vii

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Radius of a Sphere

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As much as the radius of a circle, the radius of a sphere remains mostly similar. This is because the sphere is only a 3D version of a circle. It is a directly, equidistant line segment that somewhen meets at the terminate of a sphere'south boundary.

Nevertheless, the size of a sphere is mostly based on its radius. As similar a circle, every radii drawn out from the focal betoken of the sphere has to remain the aforementioned, despite the size it attains. Luckily, we tin can approximate the volume and surface surface area past the radius of a sphere. The formulae for doing the same are,

• Radius of Sphere = 3√(3V)/4π units, (from volume)
• Radius of Sphere = √(A/4π) units (from area).

?Also read: Minors and Cofactors

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Things to Call up

• The radius of a circle is half the length of its diameter, normally meeting at the boundary of the circle.
• Interestingly, every endpoint at which the center plane meets, always remains equidistant.
• The formula of radius of a circumvolve is oftentimes denoted by "r".
• At that place are unlike formulas for different events, much like: Radius = C/2π (for circumference), Radius = √(A/π) (for area), Radius = D/2 (for diameter).
• Most circle related formulas, similar circumference and area, are adamant by commencement considering the radius.

Also read: Area of a Triangle

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Sample Questions

Ques. Determine the radius of a circle with the following points on the cartesian plane: O (two, 1), and point P (5, 5) that stands on the circumference. (iii marks)

Ans: In the given equation, the radius of a circle pointed in a cartesian airplane is expressed by the following formula: (10 − h)² + (y − k)² = rⁱⁱ

At present, after replacing the values, we get,

(five, 5) and (two, one); nosotros can become:

(5−2)ⁱⁱ + (v-1)² = r²

As per the substitution,

= three² + 4²= rⁱⁱ

= nine + 16 = r²

Therefore, r² = 25

Hence, the radius of the given circumvolve is v units.

Ques. Determine what the radius of a circumvolve will be, considering that it has a diameter of sixteen cm. (3 marks)

Ans: Given,

Diameter of the given circle= 16 cm

Now, going as per the formula we accept learnt prior, it can be determined,

Radius of the circle = D / ii (D = diameter)

Thus, Radius = xvi / ii

= viii c.one thousand.

Therefore, the radius of the given circle is viii c.thousand.

Ques. Considering the circumference of a circle as 15 inches, determine what its radius volition be? (3 marks)

Ans: As per the given equation, information technology tin can exist said that the circumference is 15 inches.

Now, it gives an thought that the post-obit formula needed to solve it will be,

R = C / 2π

Therefore, afterward replacing values,

R = fifteen / 2 π

= (15×seven) / (ii×22) (obtained after cantankerous replacing the values appropriately)

= 105 / 44 = two.39

Hence, the circumference of the circumvolve is 2.39 inches.

Ques. What is the circumference of a circle, presuming that the radius is given as 14 cm. (use the following: π = 22/vii) (3 marks)

Ans: As per the given question, we need to determine the circumference because the radius of the circle is given as = 14 c.one thousand.

At present, after using the respective formula, we can say, Circumference = 2πr units

Substituting the values, we get,

= ii * 22/seven * fourteen (since we are using π = 22/7 in the equation)

= 88 c.m

Hence, the circumference of the circle is 88 c.m, considering if its radius is 14 c.grand.

Ques. Decide a circle's equation afterwards considering its heart as (1,ii) alongside radius which is equal to 3 c.thou? (3 marks)

Ans: Equally per the given equation, the center points of the given circumvolve is (i, 2).

And, the radius is nigh three c.m.

At present, after using cartesian plane method, we become

Using the equation of the circumvolve,

(x-ane)ⁱⁱ+ (y-2)^two= 32

(10-1)ⁱⁱ+ (y-2)^two=nine

(x²- 2x + ane)+ ( yⁱⁱ -4y + iv) = nine

x² + y² - 2x -4y = 0

Therefore, the equation is as mentioned above.

Ques. Determine the approximate radius of a circle, after considering that information technology has an area of 36 yard ² . (3 marks)

Ans: In reference to the given equation, information technology says that the given surface area of the circle is 36 m^two.

Now, to determine the approximate radius of the circle, nosotros demand to use the formula listed beneath,

r = √(A/π)

Now, after substituting the values, nosotros get,

r = √36/\(\prod\)

r = √36*7/22

r = 11.45

Hence, the radius of the given circle is roughly about 11.45 meters.

Ques. What is the radius of a circle whose chord length is about 8 c.grand, besides the perpendicular distance from the focal center to the chord is iii c.thousand? (3 marks)

Ans: As per the given equation, consider the chord length to exist about = AB = 8 cm

Alongside, the perpendicular distance to be virtually = OP = three cm

Now, to find the radius, it is first important to consider its points = OA

Since nosotros are already aware that a perpendicular line commonly drawn from the center point to touch the chord often also bisects it.

Therefore, and so information technology tin be said, AP = PB = 4 c.yard

In triangle OPA,

By Pythagoras theorem,

OA² = OPⁱⁱ +AP^two

OA^two = ix +16

OA² = 25

OA = five

Hence, the answer is = 5 cm

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Source: https://collegedunia.com/exams/radius-of-a-circle-formula-and-chord-mathematics-articleid-5005

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