Circle
Curve that is radius away from centre point.
or
All points are same distance from centre.
Radius: Distance from centre to outwards only one side.
Diameter: Distance from centre to outwards on both sides.
Circumference: It is a distance once around the circle.
The ratio of circumference to the diameter is called Π.
important relation:
circumference
Centre (4,5)
Curve that is radius away from centre point.
or
All points are same distance from centre.
Radius: Distance from centre to outwards only one side.
Diameter: Distance from centre to outwards on both sides.
Circumference: It is a distance once around the circle.
The ratio of circumference to the diameter is called Π.
important relation:
circumference
↑ ×Π
Diameter
↑×2
Radius
Area of circle: It is the Π times the radius square.
i,e,
Area of circle=Πr²
Unit of Area: If the unit of the radius is meter(m) then the unit of area is meter square (m²).
Example: Find the area of circle whose radius is 3m?
Area of circle: Πr²
A=Π×r×r
A=Π×3×3
A=3.14×3×3
A=28.26m²
Lines
Chord: Chord is the line between any two points on the circumference.
Diameter: Diameter is the longest chord of the circle.
Tangent: When the line touches at only one point on the circumference, it is called tangent.
General Equation of circle
General equation of circle if (a,b) and r is the radius is given by:
(x-a)²+(y-b)²=r²
Radius=5 since it is touching the x axis hence y coordinate of center will be radius.
General equation of circle if (a,b) and r is the radius:
(x-a)²+(y-b)²=r²
(x-4)²+(y-5)²=5²
(x-4)²+(y-5)²=25
when it cut the y-axis where x=0
i.e.
(0-4)²+(y-5)²=25
16+(y-5)²=25
(y-5)²=25-16
(y-5)²=9
y-5=±3
from this
y=5+3 and 5-3
y=8 and 2
hence the circle cut the y axis at 2 and 8
The equation for a circle is x^2 + y^2 + 10y - 7 = 0. What is the centre of the circle?
Given
x²+y²+10y-7=0
General equation of circle if (a,b) and r is the radius:
(x-a)²+(y-b)²=r²
x²+y²+10y-7=0
x²+y²+10y+25=25+7
x²+(y+5)²=(√32)²
(x-a)²+(y-b)²=r²
comparing both
Centre =(0,-5)
and
Radius =√32
In a circle with a radius of 5 cm, what is the length of the chord which is at a distance of 3 cm from its center?
Given radius (r)=5cm
x²+y²+10y-7=0
x²+y²+10y+25=25+7
x²+(y+5)²=(√32)²
(x-a)²+(y-b)²=r²
comparing both
Centre =(0,-5)
and
Radius =√32
In a circle with a radius of 5 cm, what is the length of the chord which is at a distance of 3 cm from its center?
Given radius (r)=5cm
and let BAC is the chord. Midpoint is B
perpendicular from centre to chord (OA)=3cm
then BA=(√(5²-3²)=√16=4cm
length of chord (BAC)=2BA because BA=AC
length of chord (BAC)=2*4=8cm
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