ClipArt ETC
Illustration used to show that "In equal circles, or in the same circle, if two chords are equal, they are equally distant from the center; conversely, if two chords are equally distant from the center, they are equal."

Equal Chords in Equal Circles Theorem

Illustration used to show that "In equal circles, or in the same circle, if two chords are equal, they…

Illustration used to show that "In equal circles, or in the same circle, if two chords are unequal, the greater chord subtends the greater minor arc; conversely, if two minor arcs are unequal, the chord that subtends the greater arc is the greater."

Unequal Chords in Circles Theorem

Illustration used to show that "In equal circles, or in the same circle, if two chords are unequal,…

Illustration used to show that "In equal circles, or in the same circle, if two chords are unequal, the greater chord is at the less distance from the center."

Unequal Chords in Equal Circles Theorem

Illustration used to show that "In equal circles, or in the same circle, if two chords are unequal,…

Illustration used to show that "In equal circles, or in the same circle, if two chords are unequal, the greater chord is at the less distance from the center."

Unequal Chords in Equal Circles Theorem

Illustration used to show that "In equal circles, or in the same circle, if two chords are unequal,…

Illustration of eleven concentric circles.

11 Concentric Circles

Illustration of eleven concentric circles.

Illustration of eleven concentric circles.

11 Concentric Circles

Illustration of eleven concentric circles.

Circular rosette-like pattern made with 12 overlapping congruent circles tangent to a center circle and an outer circle.

12 Overlapping Circles About a Center Circle and Inside a Larger Circle

Circular rosette-like pattern made with 12 overlapping congruent circles tangent to a center circle…

Illustration of two concentric circles.

2 Concentric Circles

Illustration of two concentric circles.

Illustration of two circles that are externally tangent to each other.

2 Externally Tangent Circles

Illustration of two circles that are externally tangent to each other.

Illustration of two circles that are internally tangent to each other.

2 Internally Tangent Circles

Illustration of two circles that are internally tangent to each other.

2 congruent circles whose intersection includes a tangent circle with diameter equal to the radii of the larger circles.

2 Intersecting Circles

2 congruent circles whose intersection includes a tangent circle with diameter equal to the radii of…

Illustration showing a circle with a radius of 2 in. intersecting a circle with a radius of 3 in..

2 Intersecting Circles

Illustration showing a circle with a radius of 2 in. intersecting a circle with a radius of 3 in..

A large circle containing 2 smaller congruent circles. The small circles are externally tangent to each other and internally tangent to the larger circle. The horizontal line of centers of the small circles contains the diameter of the larger circle.

2 Smaller Horizontally Placed Circles In A Larger Circle

A large circle containing 2 smaller congruent circles. The small circles are externally tangent to each…

A large circle containing 2 smaller congruent circles. The small circles are externally tangent to each other and internally tangent to the larger circle. The vertical line of centers of the small circles contains the diameter of the larger circle.

2 Smaller Vertically Placed Circles In A Larger Circle

A large circle containing 2 smaller congruent circles. The small circles are externally tangent to each…

Circular rosette-like pattern made with 24 overlapping congruent circles tangent to a center circle and an outer circle.

24 Overlapping Circles About a Center Circle and Inside a Larger Circle

Circular rosette-like pattern made with 24 overlapping congruent circles tangent to a center circle…

Illustration of three concentric circles.

3 Concentric Circles

Illustration of three concentric circles.

A large circle containing 3 smaller congruent circles. The small circles are externally tangent to each other and internally tangent to the larger circle.

3 Smaller Circles In A Larger Circle

A large circle containing 3 smaller congruent circles. The small circles are externally tangent to each…

A large circle containing 3 smaller congruent circles. The small circles are externally tangent to each other and internally tangent to the larger circle.

3 Smaller Circles In A Larger Circle

A large circle containing 3 smaller congruent circles. The small circles are externally tangent to each…

Illustration of four concentric circles.

4 Concentric Circles

Illustration of four concentric circles.

A large circle containing 4 smaller congruent circles. The small circles are externally tangent to each other and internally tangent to the larger circle.

4 Smaller Circles In A Larger Circle

A large circle containing 4 smaller congruent circles. The small circles are externally tangent to each…

A large circle containing 4 smaller congruent circles. The small circles are externally tangent to each other and internally tangent to the larger circle.

4 Smaller Circles In A Larger Circle

A large circle containing 4 smaller congruent circles. The small circles are externally tangent to each…

Circular rosette-like pattern made with 48 overlapping congruent circles tangent to a center circle and an outer circle.

48 Overlapping Circles About a Center Circle and Inside a Larger Circle

Circular rosette-like pattern made with 48 overlapping congruent circles tangent to a center circle…

Illustration of five concentric circles.

5 Concentric Circles

Illustration of five concentric circles.

A sequence of five circles tangent to each other at a point. The radius decreases by one half in each successive circle.

5 Tangent Circles

A sequence of five circles tangent to each other at a point. The radius decreases by one half in each…

Illustration of six concentric circles.

6 Concentric Circles

Illustration of six concentric circles.

A regular hexagon containing 7 congruent circles. The circles are externally tangent to each other and internally tangent to the hexagon.

7 Congruent Circles In A Regular Hexagon

A regular hexagon containing 7 congruent circles. The circles are externally tangent to each other and…

A large circle containing 7 smaller congruent circles. The small circles are externally tangent to each other and internally tangent to the larger circle.

7 Smaller Circles In A Larger

A large circle containing 7 smaller congruent circles. The small circles are externally tangent to each…

A large circle containing 7 smaller congruent circles. The small circles are externally tangent to each other and internally tangent to the larger circle.

7 Smaller Circles In A Larger Circle

A large circle containing 7 smaller congruent circles. The small circles are externally tangent to each…

7 congruent circles. 6 of the circles are equally placed about the center circle. The circles are externally tangent to each other.

7 Tangent Circles

7 congruent circles. 6 of the circles are equally placed about the center circle. The circles are externally…

Illustration showing angles formed by two secants, two tangents, or a tangent and a secant, drawn to a circle form an external point. The angle is measured by half the difference of the intercepted arcs.

Circles With Angles Formed by Secants and Tangents

Illustration showing angles formed by two secants, two tangents, or a tangent and a secant, drawn to…

Illustration used to prove "If two circumferences meet at a point which is not on their line of centers, they also meet in one other point."

Circumferences of 2 Circles

Illustration used to prove "If two circumferences meet at a point which is not on their line of centers,…

Illustration of concentric circles.

Concentric Circles

Illustration of concentric circles.

Illustration of concentric circles used to find area between two circles (ring).

Concentric Circles (Ring) Area

Illustration of concentric circles used to find area between two circles (ring).

"If AOB is an angle of 1 ° on the larger circle, it is also 1 ° on the smaller concentric circle, and the length of the arc AB is to the length of the arc CD as to radius OB is to the radius OD; or, arc AB:arc CD = OB:OD."

Concentric Circles With Angle of 1 °

"If AOB is an angle of 1 ° on the larger circle, it is also 1 ° on the smaller concentric circle,…

Illustration of three circles enclosed in an equilateral triangle.

Circles Enclosed in Equilateral Triangle

Illustration of three circles enclosed in an equilateral triangle.

Illustration of equal circles to show that two central angles have the same ratio as their intercepted arcs.

Equal Circles With Intercepted Arcs

Illustration of equal circles to show that two central angles have the same ratio as their intercepted…

Illustrations of 2 equal circles with radii drawn.

Equal Circles With Radii

Illustrations of 2 equal circles with radii drawn.

Illustrations of 2 equal circles with radii drawn.

Equal Circles With Radii and Chords

Illustrations of 2 equal circles with radii drawn.

An illustration depicting an infinite sequence of tangent circles with the radius converging to zero. This is often called a Hawaiian earring.

Infinite Tangent Circles

An illustration depicting an infinite sequence of tangent circles with the radius converging to zero.…

Illustration of equal circles to show that an inscribed angle is measured by half the arc intercepted between its sides.

Circles With Inscribed Angles

Illustration of equal circles to show that an inscribed angle is measured by half the arc intercepted…

Illustration of a circle with a polygon (octagon) and square inscribed.

Circle With Polygon and Square Inscribed

Illustration of a circle with a polygon (octagon) and square inscribed.

Illustration of large circle and square with 4 smaller circles inside.

Circles Inside of a Square

Illustration of large circle and square with 4 smaller circles inside.

Intersecting circles with chords and radii.

Intersecting Circles

Intersecting circles with chords and radii.

Illustration of intersecting circles. "If two circles intersect each other, the line joining their centers bisects at right angles the line joining the two points of intersection."

Intersecting Circles

Illustration of intersecting circles. "If two circles intersect each other, the line joining their centers…

Illustration showing various circles and the angles formed by intersecting lines.

Intersecting Lines in Circles

Illustration showing various circles and the angles formed by intersecting lines.

Illustration of intersecting circles with a common chord.

Intersecting Circles With a Common Chord

Illustration of intersecting circles with a common chord.

Illustration showing 2 intersecting circles with a line drawn through each point of intersection terminated by the circumferences. The chords joining the ends of theses lines are parallel.

Two Intersecting Circles With Lines

Illustration showing 2 intersecting circles with a line drawn through each point of intersection terminated…

Illustration showing 2 intersecting circles with a lines drawn that form a triangle.

Two Intersecting Circles With Lines

Illustration showing 2 intersecting circles with a lines drawn that form a triangle.

Illustration of a circle with parallels intercepting equal arcs on a circumference.

Circles With Parallels Intercepting Equal Arcs

Illustration of a circle with parallels intercepting equal arcs on a circumference.

Illustration of box filled with pipes.

Circular Pipes in Box

Illustration of box filled with pipes.

Illustration of a 6-point star (convex dodecagon) inscribed in a large circle and circumscribed about a smaller circle.

Star Inscribed And Circumscribed About Circles

Illustration of a 6-point star (convex dodecagon) inscribed in a large circle and circumscribed about…

Illustration of an 8-point star (convex polygon) inscribed in a large circle and circumscribed about a smaller circle.

Star Inscribed And Circumscribed About Circles

Illustration of an 8-point star (convex polygon) inscribed in a large circle and circumscribed about…

Illustration of two circles that are tangent to each other, the line of center passing through the point of contact.

Tangent Circles

Illustration of two circles that are tangent to each other, the line of center passing through the point…

Illustration of tangent circles. One circle is said to be tangent to another circle when they touch each other at one point only.

Tangent Circles

Illustration of tangent circles. One circle is said to be tangent to another circle when they touch…

Illustration showing 2 circles with that touch each other and two lines drawn through the point of contact terminated by the circumference. The chords joining the ends of theses lines are parallel.

Tangent Circles With Chords

Illustration showing 2 circles with that touch each other and two lines drawn through the point of contact…

Projection of a circular ring.

Projection of Circular Ring

Projection of a circular ring.

A circle shape of a shield or escutcheon in heraldry.

Circular Shield

A circle shape of a shield or escutcheon in heraldry.

Illustration used to show how to pass a circumference through any three points not in the same straight line.

Construction Of Circumference

Illustration used to show how to pass a circumference through any three points not in the same straight…

The use of a compass in drawing perfect circles

Compass Use

The use of a compass in drawing perfect circles

Compass beam is used for large circles a compass or a lengthening bar cannot draw.

Beam Compass

Compass beam is used for large circles a compass or a lengthening bar cannot draw.