# 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 = **r ^{2} = *

*(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=2**r= **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 = **π**r ^{2}/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 = 2**π**r/2 = **π x **r units*

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