| {{ 'ml-lesson-number-slides' | message : article.intro.bblockCount }} |
| {{ 'ml-lesson-number-exercises' | message : article.intro.exerciseCount }} |
| {{ 'ml-lesson-time-estimation' | message }} |
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=πd
Since the diameter is twice the radius, the circumference of a circle can also be calculated by multiplying 2r by π.
C=2πr
Consider two circles and their respective diameters and circumferences.
By the Similar Circles Theorem, all circles are similar. Therefore, their corresponding parts are proportional.LHS⋅CA=RHS⋅CA
LHS/dB=RHS/dB
b1⋅a=ba
dC=π⇒C=πd
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 2πr, the arc length of each semicircle is half this value, πr.
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.
It can be noted that if the circle is divided into more and smaller sectors, then the figure will begin to look more and more like a rectangle.A=πr⋅r⇔A=πr2
It has been shown that the area of a circle is the product of π and the square of its radius.