Lesson 25. Circle and its characteristic

Lesson 25. Circle and its characteristic (Doira va uning tasnifi)

Basic information about circles

• A circle is all points in the same plane that lie at an equal distance from a center point. The circle is only composed of the points on the border. You could think of a circle as a hula hoop. It's only the points on the border that are the circle. The points within the hula hoop are not part of the circle and are called interior points.
• The distance between the midpoint and the circle border is called the radius. A line segment that has the endpoints on the circle and passes through the midpoint is called the diameter. The diameter is twice the size of the radius. A line segment that has its endpoints on the circular border but does not pass through the midpoint is called a chord.

The distance around the circle is called the circumference, C, and could be determined either by using the radius, r, or the diameter, d:

• The distance around the circle is called the circumference, C, and could be determined either by using the radius, r, or the diameter, d:
• \C=2πr\C=2πr
• C=πdC=πd
• A circle is the same as 360°. You can divide a circle into smaller portions. A part of a circle is called an arc and an arc is named according to its angle. Arcs are divided into minor arcs (0° < v < 180°), major arcs (180° < v < 360°) and semicircles (v = 180°).

The length of an arc, l, is determined by plugging the degree measure of the Arc, v, and the circumference of the whole circle, C, into the following formula:

• The length of an arc, l, is determined by plugging the degree measure of the Arc, v, and the circumference of the whole circle, C, into the following formula:
• l=C⋅v360l=C⋅v360
• When diameters intersect at the central of the circle they form central angles. Like when you cut a cake you begin your pieces in the middle.

Example

• As in the cake above we divide our circle into 8 pieces with the same angle. The circumference of the circle is 20 length units. Determine the length of the arc of each piece.
• First we need to find the angle for each piece, since we know that a full circle is 360° we can easily tell that each piece has an angle of 360/8=45°. We plug these values into our formula for the length of arcs:
• l=C⋅v360l=C⋅v360
• l=20⋅45360=2.5l=20⋅45360=2.5
• Hence the length of our arcs are 2.5 length units. We could even easier have told this by simply diving the circumference by the number of same size pieces: 20/8=2.5

• Thank you for your attention!