Parts of a circle

key Notes :

There are many parts of a circle and related circle terms. In this lesson, you will take a closer look at each of the parts and terms shown below.

Parts of a circle

Let’s take a closer look at some basic parts of a circle.

Circle and center

A circle is the set of all points that are the same distance away from a specific point, called the center.

Radius

A radius of a circle is a line segment with one endpoint at the center of the circle and the other endpoint on the circle. The plural form of radius is radii.

Diameter

A diameter of a circle is a line segment that has endpoints on the circle and passes through the center. A circle’s diameter is twice the length of the circle’s radius.

Chord

A chord of a circle is a line segment with endpoints on the circle.

Identifying parts of a circle

Let’s try it! Give an example of each of the following parts of ⨀P.

Name a radius.

PL is a radius because point P is the center of the circle and point L is on the circle. PM and PN are also radii.

Name a chord.

QR is a chord because points Q and R both lie on the circle. MN is also a chord.

Name a diameter.

MN is a diameter because points M and N both lie on the circle and MN passes through the center point.

Other circle vocabulary

You can use the parts of a circle from above to define other terms related to circles.

Central angle

A central angle of a circle is an angle whose vertex is the center of the circle and whose sides are radii of the circle.

Arc

An arc of a circle is the part of the circle that lies between two points on the circle.

Arcs can be classified as minor arcs, major arcs, or semicircles:

Minor arcs are named by their two endpoints. Major arcs and semicircles are named by their two endpoints and an additional point on the arc.

Inscribed angle and intercepted arc

An inscribed angle is an angle whose vertex is on a circle and whose sides are chords of the circle. The arc that lies between the two sides of an inscribed angle is called an intercepted arc.

Tangent and point of tangency

A tangent to a circle is a line that intersects the circle at exactly one point. The point where a tangent intersects a circle is called the point of tangency.

Circumscribed angle

A circumscribed angle is an angle whose sides are tangent to a circle.

Secant
A secant of a circle is a line that intersects the circle at two points.

Sector

A sector of a circle is a region bounded by an arc of the circle and the two radii that intersect the arc’s endpoints.

Segment

A segment of a circle is the region bounded by an arc of the circle and the chord that intersects the arc’s endpoints.

Identifying parts related to a circle

Let’s try it! Give an example of each of the following parts of the diagram below.

Name a tangent line.

NP is tangent to ⨀G because it intersects the circle at exactly one point, point H. MN is also tangent to ⨀G.

Name a major arc.

KHJ is a major arc of ⨀G because it goes more than halfway around the circle. JKH and LHK are also major arcs.

Name a central angle.

∠HGJ is a central angle of ⨀G because its vertex is the center of the circle and its sides are radii of the circle.

Name a secant line.

MP is a secant of ⨀G because it intersects the circle at two points, points J and K.

Name an inscribed angle.

∠HKJ is an inscribed angle of ⨀G because its vertex lies on the circle and its sides are chords of the circle.

Name a circumscribed angle.

∠MNP is a circumscribed angle of ⨀G because its sides are both tangent to the circle.

Name a minor arc.

HJ is a minor arc because it goes less than halfway around the circle. JK and HL are also minor arcs.

Learn with an example

let’s practice!