circle lesson formulas
Answers
2Πr...
Πr^2...
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Answer:
Step-by-step explanation:
Radius: The line segment that connects the center of the circle to any point on the circle is called radius. OB, OA, OX, OY are the different radii of the circle in the figure above. Infinite number of radii can be drawn for any circle.
Diameter: The line segment that passes through the center and connects two points on the circle is called the diameter. AB is the diameter of the circle. Like radius, infinite number of diameters can be drawn in a circle.
Diameter = 2 * radius Or
Radius = Diameter / 2
Chord: The line segment that connects any two points on a circle is a chord. Infinite number of chords can be drawn in a circle. XY is a chord of the circle.
Apparently, the diameter is the longest chord of a circle.
Circumference:
The measure of the distance around the edge of a circle is the circumference of the circle.
The circumference of a circle is given by the formula,
C = 2pr
Where C is the circumference and r is the radius.
Since 2*radius = diameter, Circumference is also given by
C = pd
The value of p is approximately 22/7 or 3.14159.
Area:
The area of a circle is given by the formula,
A = pr2
Where r is the radius of the circle.
Since r=d/2, Area is also given by
A = pd2/4
Arcs and sectors:
An arc is a part of the circumference of the circle. XY is an arc in the figure above.
A sector is the area covered by two radii and the arc connecting them. XLY and XOY are two of the sectors in the figure above.
Length of an arc is given by the formula, (x/360) * 2pr
Area of a sector is given by the formula, (x/360) * pr2
Where x is the angle subtended by the arc and r is the radius.
Central Angle: The angle whose one vertex lies on the center of the circle is a central angle. ∠XOY is a central angle in the figure above.
Inscribed angle: The angle whose one vertex lies on one part of the circle and the other two end points lie on other place on the circle, is called an inscribed angle. ∠XLY, ∠OXY, ∠OYX are some of the inscribed angles in the figure above.
Inscribed angles subtended by the same arc are equal.
A central angle is twice the corresponding inscribed angle.
In the figure above,
∠XOY = 2 ∠XLY
Tangent: A tangent of a circle is a line that just touches the circle at one point without intersecting it. MN is the tangent in the figure above.
Circumscribed circle: If a polygon is present inside a circle in such a way that all its vertices lie on the circle, or just touch the circle, then the circle is called a circumscribed circle.