Illustration showing a circle with a diameter, radius, lines, triangle, and segment drawn.

Circle With Diameter, Radius, Segment, Line

Illustration showing a circle with a diameter, radius, lines, triangle, and segment drawn.

A circle divided evenly by a dotted line.

Divided Circle

A circle divided evenly by a dotted line.

Illustration of a dodecagon circumscribed about a circle. This can also be described as a circle inscribed in a dodecagon.

Dodecagon Circumscribed About A Circle

Illustration of a dodecagon circumscribed about a circle. This can also be described as a circle inscribed…

Illustration of a dodecagon inscribed in a circle. This can also be described as a circle circumscribed about a dodecagon.

Dodecagon Inscribed In A Circle

Illustration of a dodecagon inscribed in a circle. This can also be described as a circle circumscribed…

Illustration of a circle with equal chords, which are equally distant from the center.

Circle With Equal Chords

Illustration of a circle with equal chords, which are equally distant from the center.

An illustration showing how to find the center of a circle which will pass through three given points A, B, and C. "With B as a center, draw the arc DEFG; and with the same radius and A as a center, draw the cross arcs D and F; also with C as a center, draw the cross arcs E and G. Join D and F, and also E and G, and the crossing o is the required center of the circle."

Find The Center Of A Circle Through 3 Points

An illustration showing how to find the center of a circle which will pass through three given points…

Illustration of a hexagon in a circle. Four of the six vertices of the hexagon are bound by the circle (are tangent to the circle). Because all six vertices are not on the circle, the hexagon is not cyclic; it is not inscribed in the circle.

Hexagon In A Circle

Illustration of a hexagon in a circle. Four of the six vertices of the hexagon are bound by the circle…

Illustration of hexagon inscribed in circle. Or, circle circumscribed about hexagon.

Hexagon Inscribed in Circle

Illustration of hexagon inscribed in circle. Or, circle circumscribed about hexagon.

Illustration of a circle with an angle inscribed in a segment greater than a semicircle, an acute angle.

Circle With Inscribed Angle Greater Than Semicircle

Illustration of a circle with an angle inscribed in a segment greater than a semicircle, an acute angle.

Illustration of a circle with an angle inscribed in a segment less than a semicircle, an obtuse angle.

Circle With Inscribed Angle Less Than Semicircle

Illustration of a circle with an angle inscribed in a segment less than a semicircle, an obtuse angle.

Illustration showing the diameter of a circle inscribed in a right triangle is equal to the difference between the sum of the legs and the hypotenuse.

Circle Inscribed in a Right Triangle

Illustration showing the diameter of a circle inscribed in a right triangle is equal to the difference…

Illustration of a circle with a right angle inscribed in a semicircle.

Circle With Inscribed Right Angle in Semicircle

Illustration of a circle with a right angle inscribed in a semicircle.

Illustration showing a circle with equilateral triangles and another circle within.

Circle With Triangles and Circle Within

Illustration showing a circle with equilateral triangles and another circle within.

"A circle may be conceived as a polygon of an infinite number of sides. Thus to draw the involute of a circle divide it into a convenient number of parts, draw tangents at these points, lay off on these tangents the rectified lengths of the arch from the point of tangency to the starting point, and connect the points by a smooth curve." —French, 1911

Involute of Circle

"A circle may be conceived as a polygon of an infinite number of sides. Thus to draw the involute of…

Illustration of a regular nonagon inscribed in a circle. This could also be described as a circle circumscribed about a regular nonagon.

Nonagon Inscribed in a Circle

Illustration of a regular nonagon inscribed in a circle. This could also be described as a circle circumscribed…

Illustration of circle with arc, chord, diameter  and radius.

Parts of Circle

Illustration of circle with arc, chord, diameter and radius.

Illustration of pentagon inscribed in circle. Or, circle circumscribed about pentagon.

Pentagon Inscribed in Circle

Illustration of pentagon inscribed in circle. Or, circle circumscribed about pentagon.

Illustration of circle with perpendicular diameters.

Circle With Perpendicular Diameters

Illustration of circle with perpendicular diameters.

Illustration of circle with perpendicular diameters.

Circle With Perpendicular Diameters

Illustration of circle with perpendicular diameters.

"If from any point on the circumference of a circle, a perpendicular be let fall upon a given diameter, this perpendicular will be a mean proportional between the two parts into which it divides the diameter."

Circle With a Perpendicular Drawn to the Diameter

"If from any point on the circumference of a circle, a perpendicular be let fall upon a given diameter,…

Illustration of polygon circumscribed about circle. Or, circle inscribed in the polygon.

Polygon Circumscribed About Circle

Illustration of polygon circumscribed about circle. Or, circle inscribed in the polygon.

Illustration of polygon inscribed in circle. Or, circle circumscribed about the polygon.

Polygon Inscribed in Circle

Illustration of polygon inscribed in circle. Or, circle circumscribed about the polygon.

Illustration of circle with quadrant and 60 degree arc.

Quadrant of Circle With 60 degree Arc

Illustration of circle with quadrant and 60 degree arc.

Illustration of a quadrilateral circumscribed about a circle. This could also be described as a circle inscribed in a quadrilateral.

Quadrilateral Circumscribed About a Circle

Illustration of a quadrilateral circumscribed about a circle. This could also be described as a circle…

Illustration showing a circle with a quadrilateral inscribed.

Circle With Inscribed Quadrilateral

Illustration showing a circle with a quadrilateral inscribed.

An illustration showing a quadrilateral inscribed in a circle that is tangent to a line.

Quadrilateral Inscribed In A Circle

An illustration showing a quadrilateral inscribed in a circle that is tangent to a line.

Illustration of circle with radius of 4000, and triangle with 45 degree angle enclosed.

Circles With Radius 4000 and Enclosed Triangle

Illustration of circle with radius of 4000, and triangle with 45 degree angle enclosed.

Illustration of a circle with radius QR.

Radius of a Circle

Illustration of a circle with radius QR.

An illustration showing a circle with radius r, diameter d, and chord c.

Radius, Diameter, and Chord In A Circle

An illustration showing a circle with radius r, diameter d, and chord c.

A design created by dividing a circle into 4 equal arcs and reflecting each arc toward the center of the circle. The arcs are inverted.

Reflected Arcs Of A Circle

A design created by dividing a circle into 4 equal arcs and reflecting each arc toward the center of…

Illustration of a regular heptagon/septagon inscribed in a circle. This can also be described as a circle circumscribed about a regular heptagon/septagon.

Regular Heptagon/Septagon Inscribed In A Circle

Illustration of a regular heptagon/septagon inscribed in a circle. This can also be described as a circle…

Illustration of a regular hexagon circumscribed about a circle. This can also be described as a circle inscribed in a regular hexagon.

Regular Hexagon Circumscribed About A Circle

Illustration of a regular hexagon circumscribed about a circle. This can also be described as a circle…

Illustration of a regular hexagon inscribed in a circle. This can also be described as a circle circumscribed about a regular hexagon.

Regular Hexagon Inscribed In A Circle

Illustration of a regular hexagon inscribed in a circle. This can also be described as a circle circumscribed…

Illustration of a regular hexagon inscribed in a circle. This can also be described as a circle circumscribed about a regular hexagon. All diagonals of the hexagon are also diameters of the circle. The diagonals intersect at the center of both the hexagon and the circle.

Regular Hexagon Inscribed In A Circle

Illustration of a regular hexagon inscribed in a circle. This can also be described as a circle circumscribed…

Illustration of a regular nonagon circumscribed about a circle. This can also be described as a circle inscribed in a regular nonagon.

Regular Nonagon Circumscribed About A Circle

Illustration of a regular nonagon circumscribed about a circle. This can also be described as a circle…

Illustration of a regular nonagon inscribed in a circle. This can also be described as a circle circumscribed about a regular nonagon.

Regular Nonagon Inscribed In A Circle

Illustration of a regular nonagon inscribed in a circle. This can also be described as a circle circumscribed…

Illustration of a regular octagon circumscribed about a circle. This can also be described as a circle inscribed in a regular octagon.

Regular Octagon Circumscribed About A Circle

Illustration of a regular octagon circumscribed about a circle. This can also be described as a circle…

Illustration of a regular octagon inscribed in a circle. This can also be described as a circle circumscribed about a regular octagon.

Regular Octagon Inscribed In A Circle

Illustration of a regular octagon inscribed in a circle. This can also be described as a circle circumscribed…

Illustration of a regular pentagon circumscribed about a circle. This can also be described as a circle inscribed in a regular pentagon.

Regular Pentagon Circumscribed About A Circle

Illustration of a regular pentagon circumscribed about a circle. This can also be described as a circle…

Illustration of a regular pentagon inscribed in a circle. This can also be described as a circle circumscribed about a regular pentagon.

Regular Pentagon Inscribed In A Circle

Illustration of a regular pentagon inscribed in a circle. This can also be described as a circle circumscribed…

Illustrations of a circle with secant AD and line BC tangent to it.

Circle with Secant and Point of Tangency

Illustrations of a circle with secant AD and line BC tangent to it.

Illustration of circle with sector and segment used to find area.

Circle With Sector and Segment labeled

Illustration of circle with sector and segment used to find area.

Illustration of partial circle with sector and segment used to find area.

Circle With Sector and Segment labeled

Illustration of partial circle with sector and segment used to find area.

Illustration of a sector of a circle. A sector is the space between an arc and two radii drawn to the extremities of the arc.

Sector Of Circle

Illustration of a sector of a circle. A sector is the space between an arc and two radii drawn to the…

Illustration of a sector of a hollow circle. A sector is the space between an arc and two radii drawn to the extremities of the arc.

Sector Of A Hollow Circle

Illustration of a sector of a hollow circle. A sector is the space between an arc and two radii drawn…

Illustration of circle with diameter and segment used to find area.

Circle With Diameter and Segment labeled

Illustration of circle with diameter and segment used to find area.

Illustrations of a circle with segment, semicircle, sector, quadrant, and central angles drawn.

Circle with Segment, Semicircle, Sector, Quadrant, and Central Angle

Illustrations of a circle with segment, semicircle, sector, quadrant, and central angles drawn.

Illustration of circle with segments labeled and arch.

Segments of Circle and Arch

Illustration of circle with segments labeled and arch.

Illustration of a square, with diagonals drawn, circumscribed about a circle. This can also be described as a circle inscribed in a square. The diagonals of the square intersect at the center of both the square and the circle. The diagonals coincide with the diameter of the circle.

Square Circumscribed About A Circle

Illustration of a square, with diagonals drawn, circumscribed about a circle. This can also be described…

Illustration of a square, with 1 diagonals drawn, circumscribed about a circle. This can also be described as a circle inscribed in a square. The diagonal goes through the center of both the square and the circle and coincides with the diameter of the circle.

Square Circumscribed About A Circle

Illustration of a square, with 1 diagonals drawn, circumscribed about a circle. This can also be described…

Illustration of a square circumscribed about a circle. This can also be described as a circle inscribed in a square.

Square Circumscribed About A Circle

Illustration of a square circumscribed about a circle. This can also be described as a circle inscribed…

Illustration of a square inscribed in a circle. This can also be described as a circle circumscribed about a square.

Square Inscribed In A Circle

Illustration of a square inscribed in a circle. This can also be described as a circle circumscribed…

Illustration of a square inscribed in a circle. This can also be described as a circle circumscribed about a square. The diagonal of the square is also the diameter of the circle.

Square Inscribed In A Circle

Illustration of a square inscribed in a circle. This can also be described as a circle circumscribed…

Illustration of a square, with diagonals drawn, inscribed in a circle. This can also be described as a circle circumscribed about a square. The diagonals, which are also the diameter of the circle, intersect at the center of both the square and the circle.

Square Inscribed In A Circle

Illustration of a square, with diagonals drawn, inscribed in a circle. This can also be described as…

Illustration of a 6-point star (convex dodecagon) circumscribed about a circle. This can also be described as a circle inscribed in a 6-point star, or convex dodecagon.

Star Circumscribed About A Circle

Illustration of a 6-point star (convex dodecagon) circumscribed about a circle. This can also be described…

Illustration of an 8-point star (convex polygon) circumscribed about a circle. This can also be described as a circle inscribed in an 8-point star, or convex polygon.

Star Circumscribed About A Circle

Illustration of an 8-point star (convex polygon) circumscribed about a circle. This can also be described…

Illustration of a 5-point star inscribed in a circle. This can also be described as a circle circumscribed about a 5-point star.

Star Inscribed In A Circle

Illustration of a 5-point star inscribed in a circle. This can also be described as a circle circumscribed…

Illustration of a 6-point star created by two equilateral triangles (often described as the Star of David) inscribed in a circle. This can also be described as a circle circumscribed about a 6-point star, or two triangles.

Star Inscribed In A Circle

Illustration of a 6-point star created by two equilateral triangles (often described as the Star of…

Illustration of a 6-point star (convex dodecagon) inscribed in a circle. This can also be described as a circle circumscribed about a 6-point star, or convex dodecagon.

Star Inscribed In A Circle

Illustration of a 6-point star (convex dodecagon) inscribed in a circle. This can also be described…

Illustration of an 8-point star, created by two squares at 45° rotations, inscribed in a circle. This can also be described as a circle circumscribed about an 8-point star, or two squares.

Star Inscribed In A Circle

Illustration of an 8-point star, created by two squares at 45° rotations, inscribed in a circle.…