english for siencee-circle

8/10/2019 English for Siencee-circle

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A. Definition

Circle is the set of all points in a plane that are the same distance from a fixed point

called the center.

B. Properties of A Circle

Properties Definition

Center A point inside the circle. All points on the circle are equidistant

(same distance) from the center point.

Radius (r) The radius is the distance from the center to any point on the

circle. It is half the diameter..Diameter (d) The distance across the circle. The length of any chordpassing

through the center. It is twice the radius.

Circumference (C) The circumference is the distance around the circle.

Area (A) trictly spea!ing a circle is a line" and so has no area. #hat is

usually meant is the area of the region enclosed $y the circle

Chord A line segment lin!ing any two points on a circle.

Arc An arc of a circle is the set of points on the circle that lie in the

interior of a particular central angle.

egment A segment of a circle is an area $ounded $y an arc and the chord

that connects the two endpoints of the arc. There are two

segments" mior segment and ma%or segment.

ector There are two sectors" minor sector and ma%or sector. A sector of

a circle is a region $ounded $y two radii of the circle and $y the

arc of the circle whose endpoints lie on those radii in other

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words" a sector is shaped li!e a pie slice.

Tangent A line passing a circle and touching it at %ust one point.

ecant A line that intersects a circle at two points.

&i (') The ratio of the Circumference to the Diameter of a Circle. It is

approximately equal to

3.14159265358979323846

The digits go on and on with no pattern. In fact" ' has $een

calculated to oer one trillion decimal places and still there is no

pattern.

A quic! and easy approximation to ' is **+,

**+, - 3.1428571...

ut as you can see" **+, is not exactly ri!t. In fact ' is not

equal to the ratio of any two num$ers" which ma!es it an

irrational num$er.

C. Analytic "es#lts

1. "a$i#s an$ Dia%eter

The Radius is the distance from the center to the edge. The Diameter starts at

one side of the circle" goes through the center and ends on the other side.

o the Diameter is twice the Radius

Dia%eter & 2 ' "a$i#s

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2. Circ#%ference

The Circumference is the distance around the edge of the circle.

It is exactly &i(the symbol is()times the Diameter" so

Circ#%ference & ( ' Dia%eter

And so these are also true

Circ#%ference & 2 ' ( ' "a$i#s

3. Area

The area of a circle is (times the Radius squared" which is written

A & ( ' r2

/r" in terms of the Diameter

It is easy to remem$er if you thin! of the area of the square that the circlewould fit inside.

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4. Arc )ent!

y the same reasoning" the arc length (of a

sector or segment) is

) & * ' r (when is in radians)

) & +* ' (,18- ' r (when is in degrees)

5. Area of Circle /ector0 +it! central anle

If the angle is in degrees" then

If the angle is in radians" then

D. Circle !eore%s

1. nscrie$ anle

Inscri$ed Angle is an angle made from points sitting on the circle0s

circumference

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2. Anle at Center !eore%

In a circle the angle at the center is dou$le of the angle at circumference

(inscri$ed angle)"

when angles hae the same circumference as $ase" all circumscri$ed angles

su$stending the same arc are equal irrespectie of their position on the circle.

3. Anle in a se%icircle

An angle inscrie$ in a se%icircleis always a right angle

#hy1 ecause

The insci$ed angle 234 is half

of the central angle 5634

4. Cyclic #a$rilateral

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A 7Cyclic78uadrilateralhas eery ertex on

a circle0s circumference

A Cyclic 8uadrilateral0s opposite angles addto 5634

9 a : c - 5634

9 $ : d - 5634

5. anent Anle

A tangent is a line that %ust

touches a circle at one point.

It always forms a right angle

with the circle0s radius" as

shown

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http://www.mathsisfun.com/quadrilaterals.htmlhttp://www.mathsisfun.com/quadrilaterals.html

english for siencee-circle

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