# the length of a segment from the center of a circle to its perimeter

### James

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get the length of a segment from the center of a circle to its perimeter from EN Bilgi.

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## Circle Unit Flashcards

Start studying Circle Unit. Learn vocabulary, terms, and more with flashcards, games, and other study tools.

## Circle Unit

Arc

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is a closed segment of a differentiable curve in the two-dimensional plane

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Arc Length

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The distance along the arc

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1/20 Created by Haley_Espinoza

### Terms in this set (20)

Arc

is a closed segment of a differentiable curve in the two-dimensional plane

Arc Length

The distance along the arc

Center of Circle

Center of a Circle is a point inside the circle and is at an equal distance from all of the points on its circumference.

Central Angle

The angle in a circle whose vertex is the center of the circle is called the Central Angle.

Chord

a geometric line segment whose endpoints both lie on the circle

Circle

is a simple shape of Euclidean geometry that is the set of all points in a plane that are at a given distance from a given point, the centre.

Circumference

The distance around the edge of a circle (or any curvy shape).

Diameter

A straight line going through the center of a circle connecting two points on the circumference.

Inscribed Angle

Inscribed Angle is defined as the angle formed by two chords that meet at the same point on a circle.

Intercepted Arc

That part of a circle that lies between

two lines that intersect it.

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A box contains 100 balloons. Eighty are yellow, and 20 are green. Fifty are marked "Happy Birthday!" and 50 are not. A balloon is randomly chosen from the box. How many yellow "Happy Birthday!" balloons must be in the box if the event "a balloon is yellow" and the event "a balloon is marked "Happy Birthday!" are independent?

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Let V be the volume of a sphere, S be the surface area of the sphere, and r be the radius of the sphere. Which equation represents the relationship between these three measures? A. V = rS/3 B. V = r²S/3 C. V=3/2rS D. V = 3/2r²S

Verified answer 1/6

## How to Calculate Arc Length of a Circle, Segment and Sector Area

This guide explains everything you need to know about circles, including calculation of area, segment area, sector area, length of an arc, radians, sine and cosine.

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## How to Calculate Arc Length of a Circle, Segment and Sector Area

Author: Eugene Brennan Updated date: Jan 11, 2022

Eugene is a qualified control/instrumentation engineer Bsc (Eng) and has worked as a developer of electronics & software for SCADA systems.

In this tutorial you'll learn about:

names for different parts of a circle

degrees and radians and how to convert between them

chords, arcs and secants

sine and cosine

how to work out the length of an arc and chord

how to calculate the area of sectors and segments

the equation of a circle in the Cartesian coordinate system

## What is a Circle?

"A locus is a curve or other figure formed by all the points satisfying a particular equation."

A circle is a single sided shape, but can also be described as a locus of points where each point is equidistant (the same distance) from the centre.

Circumference, diameter and radius

© Eugene Brennan

## Angle Formed by Two Rays Emanating from the Center of a Circle

An angle is formed when two lines or rays that are joined together at their endpoints, diverge or spread apart. Angles range from 0 to 360 degrees.

We often "borrow" letters from the Greek alphabet to use in math and science. So for instance we use the Greek letter "p" which is π (pi) and pronounced "pie" to represent the ratio of the circumference of a circle to the diameter.

We also use the Greek letter θ (theta) and pronounced "the - ta", for representing angles.

An angle is formed by two rays diverging from the centre of a circle. This angle ranges from 0 to 360 degrees

Image © Eugene Brennan

360 degrees in a full circle

Image © Eugene Brennan

## Parts of a Circle

A sector is a portion of a circular disk enclosed by two rays and an arc.

A segment is a portion of a circular disk enclosed by an arc and a chord.

A semi-circle is a special case of a segment, formed when the chord equals the length of the diameter.

Arc, sector, segment, rays and chord

Image © Eugene Brennan

## What is Pi (π) ?

Pi represented by the Greek letter π is the ratio of the circumference to the diameter of a circle. It's a non-rational number which means that it can't be expressed as a fraction in the form a/b where a and b are integers.

Pi is equal to 3.1416 rounded to 4 decimal places.

## What's the Length of the Circumference of a Circle?

If the diameter of a circle is D and the radius is R.

Then the circumference C = πD

But D = 2R Scroll to Continue

## Read More From Owlcation

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Read More From Owlcation Calculating the Centroid of Compound Shapes Using the Method of Geometric Decomposition How to Calculate Bolt Circle Diameter (BCD) for Chainrings and Bash Guards Calculator Techniques for Circles and Triangles in Plane Geometry

So in terms of the radius R

C = πD = 2πR

## What's the Area of a Circle?

The area of a circle is A = πR2

But R = D/2

So the area in terms of the radius R is

A = πR2 = π (D/2)2 = πD2/4

## What are Degrees and Radians?

Angles are measured in degrees, but sometimes to make the mathematics simpler and elegant it's better to use radians which is another way of denoting an angle. A radian is the angle subtended by an arc of length equal to the radius of the circle. ( "Subtended" means produced by joining two lines from the end points of the arc to the center).

An arc of length R where R is the radius of a circle, corresponds to an angle of 1 radian

So if the circumference of a circle is 2πR i.e 2π times R, the angle for a full circle will be 2π times 1 radian or 2π radians.

And 360 degrees = 2π radians

A radian is the angle subtended by an arc of length equal to the radius of a circle.

Image © Eugene Brennan

## How to Convert From Degrees to Radians

360 degrees = 2π radians

Dividing both sides by 360 gives

1 degree = 2π /360 radians

Then multiply both sides by θ

θ degrees = (2π/360) x θ = θ(π/180) radians

So to convert from degrees to radians, multiply by π/180

## How to Convert From Radians to Degrees

2π radians = 360 degrees

Guys, does anyone know the answer?