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A circle is the set of all the points in a plane that are equidistant from a given point. There are a few particularly notable features of a circle.
circle O,since it is centered at O.
The circumference of a circle is calculated by multiplying its diameter by π.
C=π d
Since the diameter is twice the radius, the circumference of a circle can also be calculated by multiplying 2r by π.
C=2π r
Consider two circles and their respective diameters and circumferences.
LHS * C_A=RHS* C_A
.LHS /d_B.=.RHS /d_B.
1/b* a = a/b
C/d=π ⇒ C=π d
The area of a circle is the product of π and the square of its radius.
A circle with radius r will be divided into a number of equally sized sectors. Then, the top and bottom halves of the circle will be distinguished by filling them with different colors. Because the circumference of a circle is 2 π r, the arc length of each semicircle is half this value, π r.
Now, the above sectors will be unfolded. By placing the sectors of the upper hemisphere as teeth pointing downwards and the sectors of the bottom hemisphere as teeth pointing upwards, a parallelogram-like figure can be formed. As such, the area of the figure below should be the same as the circle's area.
A = π r * r ⇔ A= π r^2
It has been shown that the area of a circle is the product of π and the square of its radius.
In the diagram, AP is tangent ray and AP is tangent segment. A tangent is always perpendicular to a radius in the circle.
A line that intersects a circle in two places is called a secant.