This document defines key terms and formulas related to circles, including the circumference, diameter, radius, area, arcs, sectors, segments, chords, and semicircles. Circumference is defined as 2πr or πd. Area of a circle is πr^2. Arc length formulas are given for degrees and radians. Sector area formulas are also provided for degrees and radians. Formulas are provided for finding the length of a chord given the radius and central angle or radius and distance to the center. The perimeter and area formulas for a semicircle are defined as well. Examples are included to demonstrate the application of each formula.
Areas related to circles - perimeter and area of a circle for class 10 maths.Let's Tute
In this video you will learn Areas related to circles - perimeter and area of a circle
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Areas related to circles - perimeter and area of a circle for class 10 maths.Let's Tute
In this video you will learn Areas related to circles - perimeter and area of a circle
To watch more such videos -
Visit - www.letstute.com
YouTube - www.youtube.com/letstute
Thank you
Areas related to circles - Perimeter and area of a circle for class 10 maths.Let's Tute
Areas related to circles - Perimeter and area of a circle for class 10 maths.
Let's tute is an E-school or E- platform which is free for the student.Students will watch "MATHS" Videos for conceptual understanding.
Areas related to circles - Perimeter and area of a circle for class 10 maths.Let's Tute
Areas related to circles - Perimeter and area of a circle for class 10 maths.
Let's tute is an E-school or E- platform which is free for the student.Students will watch "MATHS" Videos for conceptual understanding.
ESCUELA SEGURA LUCHANDO CONTRA LA DELINCUENCIAAlicia Elizondo
Concientizar a los padres de familia para evitar la delincuencia que impera en el entorno escolar mediante talleres tecnológicos que movilice el espíritu de mejora en la comunidad, empezando con la implementación de valores en preescolar.”
Learn about the properties of tangents, chords and arcs of the circle. Learn to find measure of the inscribed angle and the property of cyclic quadrilateral
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CIRCLE
DEFINITION AND PROPERTIES OF A CIRCLE
A circle can be defined in two ways.
A circle: Is a closed path curve all points of which are equal-distance from a fixed point called centre OR
- Is a locus at a point which moves in a plane so that it is always of constant distance from a fixed point known as a centre.
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The French Revolution, which began in 1789, was a period of radical social and political upheaval in France. It marked the decline of absolute monarchies, the rise of secular and democratic republics, and the eventual rise of Napoleon Bonaparte. This revolutionary period is crucial in understanding the transition from feudalism to modernity in Europe.
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Ethnobotany in herbal drug evaluation,
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We all have good and bad thoughts from time to time and situation to situation. We are bombarded daily with spiraling thoughts(both negative and positive) creating all-consuming feel , making us difficult to manage with associated suffering. Good thoughts are like our Mob Signal (Positive thought) amidst noise(negative thought) in the atmosphere. Negative thoughts like noise outweigh positive thoughts. These thoughts often create unwanted confusion, trouble, stress and frustration in our mind as well as chaos in our physical world. Negative thoughts are also known as “distorted thinking”.
1. CIRCLE
Prepared by : Pang Kai Yun, Sam Wei Yin,
Ng Huoy Miin, Trace Gew Yee,
Liew Poh Ka, Chong Jia Yi
2. CIRCLE
A circle is a plain figure enclosed by a curved line,
every point on which is equidistant from a point
within, called the centre.
3. DEFINITION
Circumference - The circumference of a
circle is the perimeter
Diameter - The diameter of a circle is longest
distance across a circle.
Radius - The radius of a circle is the distance
from the center of the circle to the outside
edge.
11. EXAMPLE 1 (ARC LENGTH)
𝑙 𝑎 =
𝑛
360 𝑜 2𝜋r
=
45 𝑜
360 𝑜 x 2 x 3.142 x 12
=
1
8
x 75.41
= 9.43 cm
12. RADIAN
The angle made by taking the radius and
wrapping it along the edge of the circle.
13. FROM RADIAN TO DEGREE
Degree =
180 𝑜
π
x Radians
Radians =
π
180 𝑜 x Degree
FROM DEGREE TO RADIAN
14. EXAMPLE (FROM RADIAN TO DEGREE)
1.
π
3
rad =
180 𝑜
π
x
π
3
rad = 60 𝑜
2.
2π
3
rad =
180 𝑜
π
x
2π
3
rad = 120 𝑜
3.
5π
4
rad =
180 𝑜
π
x
5π
4
rad = 225 𝑜
15. EXAMPLE (FROM DEGREE TO RADIAN)
1. 30 𝑜
=
π
180 𝑜 x 30 𝑜
=
π
6
rad
3. 270 𝑜
=
π
180 𝑜 x 270 𝑜
=
3π
2
rad
2. 150 𝑜
=
π
180 𝑜 x 150 𝑜
=
5π
6
rad
26. EXAMPLE (AREA OF SEGMENT)
Solution:
(i) 𝑙 𝑎 = 8 cm
𝑙 𝑎 = r θ
8 = r θ
8 = 6 θ
θ = 1.333 radians
Ð AOB = 1.333 radians
The above diagram shows a sector of a
circle, with centre O and a radius 6 cm.
The length of the arc AB is 8 cm. Find
(i) Ð AOB
(ii) the area of the shaded segment.
(ii) the area of the shaded segment
1
2
𝑟2(θ - sin θ)
=
1
2
(6)2(1.333 - sin 1.333)
=
1
2
(36)(1.333 – 0.927)
= 6.498 cm2
27. CHORD
Chord of a circle is a line segment whose ends
lie on the circle.
30. GIVEN THE RADIUS AND DISTANCE TO CENTER
This is a simple application of Pythagoras'
Theorem.
Chord length = 2 𝑟2 − 𝑑2
31. EXAMPLE 2
Find the chord of the circle where the radius
measurement is about 8 cm that is 6 units from the
middle.
Solution:
Chord length = 2 𝑟2 − 𝑑2
= 2 82 − 62
= 2 64 − 36
= 2 28
= 10.58 cm
33. PERIMETER OF A SEMICIRCLE
Remember that the perimeter is the distance
round the outside. A semicircle has two edges.
One is half of a circumference and the other is
a diameter
So, the formula for the perimeter of a semicircle
is:
Perimeter = πr + 2r
35. AREA OF A SEMICIRCLE
A semicircle is just half of a circle. To find the
area of a semicircle we just take half of the
area of a circle.
So, the formula for the area of a semicircle is:
Area =
1
2
π𝑟2