GCSE Circle
Circle:
A circle is a locus of all points which are at the same distance from the fixed point. This distance from the center to each point is called the radius.
Different parts of a circle:
Centre: Centre of a circle is the point that is equidistant from all points of the circle.
Radius: A line from the center of a circle to the circumference of a circle.
Diameter: Diameter is a line that passes through the center of the circle and whose endpoints lie on the circle.
Diameter (d) = 2 x radius
Chord: A Chord is a line segment that connects two points present on the circumference of the circle. If the chord passes through the center of the circle, then it is called the diameter.
Tangent: A line that touches the circumference of a circle at any one point is called Tangent.
Arc (Major and Minor): A small part of the circumference of a circle.
Sector (Major and Minor): A part of the circle enclosed by two radii (r1 and r2) of the circle. A sector means a portion of the circle. The arc is just part of the circumference, but the sector is part of the area.
Area of a Circle:
The amount of space occupied by the circle is defined as the area of a circle.
Area = r2 = (square units)
Where r= radius
d=diameter=2r
Circumference of the Circle:
Distance around the circle is defined as circumference of a circle.
Circumference of a circle, C=2r= d (units)
Where r= radius
d=diameter
d=2r
Semi-Circle:
A semi-circle is formed when the circle is divided into two parts.
Area of Semicircle:
The area of a semicircle is equal to half of the area of the circle.
Area of semicircle, A = πr2/2 square units
Circumference of Semicircle:
Circumference or perimeter of a semicircle is equal to the half of the circumference of the circle.
Circumference of the semicircle, C = 2πr/2 = π x r units
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