ClipArt ETC
An illustration showing how to construct a pentagon inscribed in a circle. "Draw the diameter AB, and from the center C erect the perpendicular CD. Bisect the radius AC at E; with E as center, and DE as radius, draw the arc DE, and the straight line DF is the length of the side of the pentagon."

Construction Of A Pentagon Inscribed In A Circle

An illustration showing how to construct a pentagon inscribed in a circle. "Draw the diameter AB, and…

An illustration showing how to construct a pentagon on a given line. "From B erect BC perpendicular to and half the length of AB; join A and C prolonged to D; with C as center and CB as radius, draw the arc BD; then the chord BB is the radius of the circle circumscribing the pentagon. With A and B as centers, and BD as radius, draw the cross O in the center."

Construction Of A Pentagon On A Line

An illustration showing how to construct a pentagon on a given line. "From B erect BC perpendicular…

Illustration of a cyclic pentagon, a pentagon inscribed in a circle. This can also be described as a circle circumscribed about a pentagon. In this illustration, the pentagon is not regular (the lengths of the sides are not equal).

Cyclic Pentagon

Illustration of a cyclic pentagon, a pentagon inscribed in a circle. This can also be described as a…

Diagram used to prove the theorem: "A plane perpendicular to a radius at its extremity is tangent to the sphere."

Sphere Tangent to Plane

Diagram used to prove the theorem: "A plane perpendicular to a radius at its extremity is tangent to…

Two arrangements of pulley: crossed belt and uncrossed belt. The pulleys are constructed with two circles that have the radii labeled and tangent lines drawn (strings).

Pulley

Two arrangements of pulley: crossed belt and uncrossed belt. The pulleys are constructed with two circles…

Illustration of an angle &alpha with the vertex at the center, O, of a circle with radius OB. AC and BD are perpendicular to OB and join B with C. The are of the triangle OBC is less than the are of the sector OBC, and the sector OBC is less than the triangle OBD.

Triangles and Sectors in Quadrant I

Illustration of an angle &alpha with the vertex at the center, O, of a circle with radius OB. AC and…

Illustration of an angle &alpha with the terminal side used to draw a triangle in quadrant I.

Triangle in Quadrant I

Illustration of an angle &alpha with the terminal side used to draw a triangle in quadrant I.

Illustration of an angle with the terminal side used to draw a triangle in quadrant II.

Triangle in Quadrant II

Illustration of an angle with the terminal side used to draw a triangle in quadrant II.

Illustration of a cyclic quadrilateral, a quadrilateral inscribed in a circle. This can also be described as a circle circumscribed about a quadrilateral. In this illustration, the quadrilateral is not regular (the lengths of the sides are not equal).

Cyclic Quadrilateral

Illustration of a cyclic quadrilateral, a quadrilateral inscribed in a circle. This can also be described…

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

Regular Heptagon/Septagon Circumscribed about a Circle

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

A secant is "a line which cuts a figure in any way. Specifically, in trigonometry, a line from the center of a circle through one extremity of an arc (whose secant it is said to be) to the tangent from the other extremity of the same arc; or the ratio of this line to the radius; the reciprocal of the cosine. The ratio of AB to AD is the secant of the angle A; and AB is the secant of the arc CD." —Whitney, 1889

Circle with Secant

A secant is "a line which cuts a figure in any way. Specifically, in trigonometry, a line from the center…

An illustration showing how to construct a square circumscribed about a circle. "Draw the diameters AB and CD at right angles to one another; with the radius of the circle, and A, B, C, and D as centers, draw the four dotted half circles which cross one another in the corners of the square, and thus complete the problem."

Construction Of A Square Circumscribed About A Circle

An illustration showing how to construct a square circumscribed about a circle. "Draw the diameters…

An illustration showing how to construct a square inscribed in a circle. "Draw the diameter AB, and through the center erect the perpendicular CD, and complete the square as shown in the illustration."

Construction Of A Square Inscribed In A Circle

An illustration showing how to construct a square inscribed in a circle. "Draw the diameter AB, and…

Illustration of a giant stepladder, sometimes called a skyscraper stepladder, that is opened next to a palm tree. One of the bottom legs of the unfolded ladder is adjacent to the tree. The ladder forms an isosceles triangle with the ground.

Skyscraper Giant Stepladder

Illustration of a giant stepladder, sometimes called a skyscraper stepladder, that is opened next to…

An illustration showing how to construct a talon, or two circle arcs that will tangent themselves, and meet two parallel lines at right angles in the given points A and B. "Join A and B; divide AB into four equal parts erect perpendiculars; then m and n are the centers of the circle arcs of the required talon."

Construction Of A Talon

An illustration showing how to construct a talon, or two circle arcs that will tangent themselves, and…

Illustration of point of tangency (line and circle).

Point of Tangency

Illustration of point of tangency (line and circle).

Illustration of radius drawn to point of contact of a tangent.

Point of Tangency

Illustration of radius drawn to point of contact of a tangent.

An illustration showing how to construct a tangent between 2 given circles. "Join the centers C and c of the given circles; draw the dotted circle arcs, and join the crossing m, n, which line cuts the center line at a. With aC as diameter, draw the half circle afC; and with ac as a diameter, draw the half circle cea; then the crossings e and f are the tangenting points of the circles."

Construction Of Tangent Between 2 Circles

An illustration showing how to construct a tangent between 2 given circles. "Join the centers C and…

An illustration showing how to construct a tangent to 2 given circles of different diameters. "Join the centers C and c of the given circles, and extend the line to D; draw the radii AC and ac parallel with one another. Join Aa, and extend the line to D. On CD as a diameter, draw the half circle CeD; on cD as a diameter, draw the half circle cfD; then the crossings e and f are the tangenting points of the circles."

Construction Of Tangent To 2 Circles

An illustration showing how to construct a tangent to 2 given circles of different diameters. "Join…

An illustration showing how to construct a tangent circle to 2 given circles. "Join centers C and c of the given circles, and extend the line to D; draw the radii AC and ac parallel with one another. Join Aa, and extend the line to D. On CD as a diameter, draw the half circle CeD; on cD as a diameter, draw the half circle cfD; then the crossings e and f are tangenting points of the circles."

Construction Of Circle Tangent To 2 Circles

An illustration showing how to construct a tangent circle to 2 given circles. "Join centers C and c…

Illustration used to draw a tangent to a circle.

Construction of Tangent to a Circle

Illustration used to draw a tangent to a circle.

An illustration showing how to construct a tangent to a circle through a given point in a circumference. "Through a given point A and center C, draw the line BC. With A as a center, draw the circle arcs B and C; with B and C as centers, draw the cross arcs D and E; then join D and E, which is the required tangent."

Construction Of Tangent To Circle

An illustration showing how to construct a tangent to a circle through a given point in a circumference.…

An illustration showing how to construct a tangent to a circle through a given point outside of a circumference. "Join A and C, and upon AC as a diameter draw the half circle ABC, which cuts the given circle at B. Join A and B, which is the required tangent."

Construction Of Tangent To Circle

An illustration showing how to construct a tangent to a circle through a given point outside of a circumference.…

An illustration showing how to construct a tangent circle to a circle with a given radius. "Through the given point C, draw the diameter AC extended beyond D: from C set off the given radius R to D; then D is the center of the required circle, which tangents the given circle at C."

Construction Of Circle Tangent To Circle

An illustration showing how to construct a tangent circle to a circle with a given radius. "Through…

Trigonometric reference triangles/angles drawn for 60 degree reference angel in quadrants I and II.

Trigonometric Reference Triangles/Angles (60 degrees) Drawn in Quadrants

Trigonometric reference triangles/angles drawn for 60 degree reference angel in quadrants I and II.

Trigonometric reference triangles/angles drawn for reference angel in quadrants I and II. This illustration could be used to find trig ratios.

Trigonometric Reference Triangles/Angles Drawn in Quadrants

Trigonometric reference triangles/angles drawn for reference angel in quadrants I and II. This illustration…

Right triangle OCA, inside of Circle O is used to show that side AC is "opposite" O and side OC is "adjacent" to O. OA is the hypotenuse. Sine is defined as the ratio of the opposite side to the hypotenuse (AC/OA). Cosine is defined as the ratio of the adjacent side to the hypotenuse (OC/OA), and Tangent is defined as the ratio of the opposite side to the adjacent side (DB/OB).

Trigonometry Triangle to Show Sine, Cosine, and Tangent

Right triangle OCA, inside of Circle O is used to show that side AC is "opposite" O and side OC is "adjacent"…

An illustration showing how to construct two circles that tangent themselves and two given lines. "Draw the center line AB between the given lines; assume D to be the tangenting point of the circles; draw DC at right angles to AB. With C as center and CD as radius, draw the circle EDF. From E, draw Em at right angles to EF; and from F draw Fm at right angles to FE; then m and n are the centers for the required circles."

Construction Of Two Circles That Tangent Themselves and 2 Given Lines

An illustration showing how to construct two circles that tangent themselves and two given lines. "Draw…