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Circle: Diameter, Chord, Radius, Arc, Tangent




In this lesson, we will learn the following parts of a circle: diameter, chord, radius, arc and tangent

We will also learn about congruent circles, concentric circles and intersecting circles.

Related Topics: More Geometry Lessons

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.

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.

diameter

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.

chord



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.

radius

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

Arc

An arc is a part of a circle.

arc

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 ancle symbolBOC 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.

tangent

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 OB. Point B is called the point of tangency.

BCis perpendicular to OB i.e. BC perpendicular to OB


 



Parts of a Circle

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.

Congruent and Concentric Circles

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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