Circles
• A circle consists of all the points that are the same distance from one fixed point called the center. That distance is called the radius of a circle. The word radius is also used to represent any of the line segments joining the center and a point on the circle. The plural of radius is radii.
• Any triangle formed by connecting the end points of two radii, is an isosceles.
• A line segment both of whose end points are on a circle is called a chord.
• A chord that passes through the center of the circle is called the diameter of the circle. The length of the diameter is always double the radius of the circle. The diameter is the longest cord that can be drawn in a circle.
• The total length around a circle is known as the circumference of the
circle.
• The ratio of the circumference to the diameter is always the same for any circle. This ratio is denoted by the symbol
π (pronounced as pi).
•
π = C/d ⇒ C = πd ⇒ C = 2πr where C is the circumference, d is the diameter and r is the radius of the circle.
• Value of
π is approximately
3.14.
• An arc consists of two points in a circle and all the points between them.
• An angle whose vertex is at the center of the circle is called the central angle.
• The degree measure of a complete circle is
360°.
• The degree measure of an arc is the measure of the central angle that intercepts it.
• If x is the degree measure of an arc, its length can be calculated as x/360 * C where C is the circumference.
• The area of a circle can be calculated as
πr^2 .
• The area of a sector formed by the arc and two radii can be calculated as x/360 * A, where A is the area of a circle.
Continued...