The circle is a location of a point that progresses at a regular distance from a fixed point. These fixed points are called the centre of the circle and this regular distance is called a Radius. If we consider r as the radius of the circle the diameter becomes d=2r.
Diameter is the maximal distance between any of the two points given in a particular circle.
Hence we can split up the diameter into two parts first from any endpoint of a circle to the centre and second from the centre to another endpoint on the circle.
The word circle is the origin from Greek which means kirkos, hoop, or ring.
General Equation of Circle:-
x²+y²+2gx+2fy+c=0 is the general equation of a circle, in which g, f, c, are constants.
The middle point of the circle is (-g, -f) that is -½ coefficient of x and -½ coefficient of y.
If the radius of the circle is equal to r then r=
If the radius r of the given circle x²+y²+2gx+2fy+c=0 touches the x and y-axis then g²=c and f²=c respectively.
Angle delimited at a centre of a circle by an arc given by arc/radius.
Circles Sample Questions for Class 11
Question 1
A sculptor is commissioned to carve a granite block into a cone shape which weighs 5000 \ "lb". The finished height needs to be 5 \ "ft". Knowing that granite weighs about 165 \ "lb"//"ft"^3, what will be the finished diameter of the sculpture?
A. 4.8 \ "ft"
B. 2.6 \ "ft"
C. 13.2 \ "ft"
D. 2.3 \ "ft"
Question 2
The method used in the previous questions is the only way to derive the equation of a circle.
A. True
B. False
Question 3
The arc length around a unit circle has the same value as the arc angle, in radians, that it subtends.
A. True
B. False
Question 4
Thus far, only a circle of radius 1/2 was used. Which of the following formulas would correctly relate this circle with a new circle of unknown circumference, C, and radius, r. Why?
A. C/pi = r/(1/2) because all circles are similar.
B. C=1/2 r pi since the new circle will depend on the measurements of the circle already investigated.
C. C/2 = pi r^2 because the area of a circle is related to its circumference.
D. C = npi, r=n/2 since the new circle's circumference and radius will depend upon the number of sides of an inscribed regular polygon.
Question 5
An arc length of 2.62 m on a circle with a radius of 1 m would subtend and arc angle of how many radians?
A. pi/2
B. (5pi)/3
C. (5pi)/6
D. (7pi)/6