Geometry: Circles

In geometry, a circle is a closed curve formed by a set of points on a plane that are the same distance from its center O. That distance is known as the radius of the circle.

Diameter

The diameter of a circle is a line segment that passes through the center of the circle and has its endpoints on the circle. All the diameters of the same circle have the same length.

A chord is also a line segment with both endpoints on the circle, but it may not pass through the center of the circle.

Radius

The radius of the circle is a line segment from the center of the circle to a point on the circle.

In the above diagram, O is the center of the circle and and  are radii of the circle. The radii of a circle are all the same length. The radius is half the length of the diameter.

Arc

An arc is a part of a circle.

In the diagram above, the part of the circle from B to C forms an arc.

An arc can be measured in degrees.

In the circle above, arc BC is equal to the BOC that is 45°.

Tangent

A tangent is a line that touches a circle at only one point. A tangent is perpendicular to the radius at the point of contact.

In the above diagram, the line containing the points B and C is a tangent to the circle.

It touches the circle at point B and is perpendicular to the radius

is perpendicular to  i.e.

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