Circle: Diameter, chord, radius, arc, tangent

In this lesson, we will learn the following parts of a circle

• diameter
• chord
• radius
• arc
• tangent

We will also learn about

• congruent circles
• concentric circles
• intersecting circles

Circle

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.

Chord

A chord is a line segment with both endpoints on the circle. The diameter is a special chord that passes through the center of the circle. The diameter would be the longest chord in the circle.

Radius

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

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. The point of tangency is where a tangent line touches the circle.

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 . Point B is called the point of tangency.

is perpendicular to  i.e.

The following video gives the definitions of a circle, a radius, a chord, a diameter and a secant.

The following video describe the different parts of a circle: chord, diameter, radius & circumference.

The following video explains the parts of a circle, including center point, radius, chord, diameter, central angle, arc, and sector.

Congruent Circles

Congruent circles are circles that have the same radius, but different centers.

Concentric Circles

Concentric circles are circles that have the same center, but have a different radii.

Intersecting Circles

Two circles may intersect at two points or at one point. If they intersect at one point then they can either be externally tangent or internally tangent.

Two circles that do not intersect can either have a common external tangent or common internal tangent. In the common external tangent, the tangent does not cross between the two circles. In the common internal tangent, the tangent crosses between the two circles.

This video introduces the features of circles including secant, secant line, chord, diameter, radius, tangent line, and intersecting circles.

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