Geometric Constructions | ClipArt ETC

This mathematics ClipArt gallery offers 213 illustrations of common geometric constructions. Geometric constructions are made with only the use of a compass and a straight edge. In addition to the constructions of different types of polygons, images include those used to show how to bisect a line, angle, and arc.

Illustration showing how to construct the bisector of an angle.

Construction Of Angle Bisector

Illustration showing how to construct the bisector of an angle.

Illustration used to show how to "draw a straight line through any given point on a given straight line to make any required angle with that line."

Construction Of Angle On Straight Line

Illustration used to show how to "draw a straight line through any given point on a given straight line…

Illustration used to show how to construct a bisector of an angle when the sides intersect within the limits of the drawing.

Bisect An Angle

Illustration used to show how to construct a bisector of an angle when the sides intersect within the…

Illustration used to show how to construct a bisector of an angle when the sides no not intersect within the limits of the drawing.

Bisect An Angle

Illustration used to show how to construct a bisector of an angle when the sides no not intersect within…

Illustration of construction to lay off an angle.

Construction of Angle

Illustration of construction to lay off an angle.

An illustration showing the construction used to divide an angle into two equal parts. "With C as a center, draw the dotted arc DE; with D and E as centers, draw the cross arcs at F with equal radii. Join CF, which divides the angle into the required parts."

Construction Of A Divided Angle

An illustration showing the construction used to divide an angle into two equal parts. "With C as a…

An illustration showing the construction used to divide an angle into two equal parts when the lines do not extend to a meeting point. "Draw the lined CD and CE parallel, and at equal distances from the lines AB and FG. With C as a center, draw the dotted arc BG; and with B and G as centers, draw the cross arcs H. Join CD, which divides the angle into the required equal parts."

Construction Of A Divided Angle

An illustration showing the construction used to divide an angle into two equal parts when the lines…

"When the minor axis is at least two-thirds the major, the following method ma be used:Make CF and CG equal to AB-DE.Make CH and CI equal to 3/4 CFF, G, H, I will be centers for arcs E, D, B, and A." —French 1911

Approximate Ellipse using Lines

"When the minor axis is at least two-thirds the major, the following method ma be used: Make CF and…

"This (five centered arc) method is based on the principle that the radius of curvature at the end of the minor axis is the third proportional to the semi-minor and semi-major axes, and similarly at the end of the major axis is the third proportional to the semi-major and semi-minor axes. The intermediate radius found is the mean proportional between these two radii." —French, 1911

Approximate Ellipse with Five Centered Arc

"This (five centered arc) method is based on the principle that the radius of curvature at the end of…

"Join A and D. Lay off DF equal to AC-DC. Bisect AF by a perpendicular crossing AC at G and intersecting DE produced at H. Make CG' equal to CG and CH' equal to CH. Then G, G', H, and H' will be centers for four arcs approximating the ellipse. The half of this ellipse when used in masonry construction is known as the three-centered arch." —French, 1911

Approximate Ellipse with Four Centers

"Join A and D. Lay off DF equal to AC-DC. Bisect AF by a perpendicular crossing AC at G and intersecting…

"At A draw the tangent AD and Chord AB produced. Lay off AC equal to half the chord AB. With center C and radius CB draw an arc intersecting AB at E, then AE will be equal in length be to the arc AB." —French, 1911

Approximating Length of Circle Arc using Straight Line

"At A draw the tangent AD and Chord AB produced. Lay off AC equal to half the chord AB. With center…

"Draw lines parallel to AB and CD at distant R from them. The intersection of these lines will be center of the required arc." —French, 1911

Draw Arc of Given radius R Tangent to Two Given Lines

"Draw lines parallel to AB and CD at distant R from them. The intersection of these lines will be center…

Illustration used to show how to bisect a given arc.

Bisecting an Arc

Illustration used to show how to bisect a given arc.

Illustration used to show how to "find an arc of a circle having a known radius, which shall be equal in length to a given straight line."

Construction Of Arc

Illustration used to show how to "find an arc of a circle having a known radius, which shall be equal…

"Divide the circumference into a number of equal parts, drawing the radii and numbering the points. Divide the radius No. 1 into the same number of equal parts, numbering from the center. With C as center draw concentric arcs intersecting the radii of corresponding numbers, and draw a smooth curve through these intersections." —French, 1911

Draw Spiral of Archimedes

"Divide the circumference into a number of equal parts, drawing the radii and numbering the points.…

Method to draw the bisector of a line

Bisect A Line

Method to draw the bisector of a line

Method to bisect an angle

Bisect An Angle

Method to bisect an angle

An illustration showing how to construct the center and radius of a circle that will tangent a given circle and line. "Through the given point C, draw the line EF at right angles to AB; set off from C the radius r of the given circle. Join G and F. With G and F as centers draw the arc crosses m and n. Join mn, and where it crosses the line EF is the center of the required circle."

Construction Of A Center And Radius Of A Circle That Will Tangent A Given Circle And Line

An illustration showing how to construct the center and radius of a circle that will tangent a given…

An illustration showing how to construct the center and radius of a circle that will tangent a given circle and line. "From C, erect the perpendicular CG; set off the given radius r from C to H. With H as a center and r as radius, draw the cross arcs on the circle. Through the cross arcs draw the line IG; then G is the center of the circle arc FIC, which tangents the line at C and the circle at F."

Construction Of A Center And Radius Of A Circle That Will Tangent A Given Circle And Line

An illustration showing how to construct the center and radius of a circle that will tangent a given…

An illustration showing how to construct the center and radius of a circle that will tangent a given circle. "Through the given point C, draw the tangent GF; bisect the angle FGE; then o is the center of the required circle that will tangent AB at C, and the line DE."

Construction Of A Center And Radius Of A Circle That Will Tangent A Given Circle

An illustration showing how to construct the center and radius of a circle that will tangent a given…

An illustration showing how to construct a center and radius of a circle that will tangent the three sides of a triangle. "Bisect two of the angles in the triangle, and the crossing C is the center of the required circle."

Construction Of The Center And Radius Of A Circle Tangent To Triangle Sides

An illustration showing how to construct a center and radius of a circle that will tangent the three…

Illustration used to show how to find the center when given an arc and its radius.

Construction Of Center

Illustration used to show how to find the center when given an arc and its radius.

An illustration showing how to construct a circle arc without recourse to its center, but its chord AB and height h being given. "With the chord as radius, and A and B as centers, draw the dotted circle arcs AC and BD. Through the point O draw the lines AOo and BOo. Make the arcs Co=Ao and Do=Bo. Divide these arcs into any desired number of equal parts, and number them as shown on the illustration. Join A and B with the divisions, and the crossings of equal numbers are points in the circle arc."

Construction Of A Circle Arc

An illustration showing how to construct a circle arc without recourse to its center, but its chord…

Illustration used to construct a circle when given three points.

Construction of Circle Given 3 Points

Illustration used to construct a circle when given three points.

An illustration showing how to construct a circle tangent to a given line and given circle. "Add the given radius r to the radius R of the circle, and draw the arc cd. Draw the line ce parallel with and at a distance r from the line AB. Then the crossing c is the center of the required circle that will tangent the given line and circle."

Construction Of A Circle Tangent To A Line And A Circle

An illustration showing how to construct a circle tangent to a given line and given circle. "Add the…

An illustration showing how to construct a circle that tangents two given lines and goes through a given point c on the line FC, which bisects the angle of the lines. "Through C draw AB at right angles to CF; bisect the angles DAB and EBA, and the crossing on CF is the center of the required circle."

Construction Of A Circle That Tangents 2 Given Lines And Goes Through A Given Point

An illustration showing how to construct a circle that tangents two given lines and goes through a given…

An illustration showing how to construct a circle that tangents two given lines inclined to one another with the one tangenting point being given. "Draw the center line GF. From E, draw EF at right angles to AB; then F is the center of the circle required.

Construction Of A Circle That Tangents 2 Given Lines

An illustration showing how to construct a circle that tangents two given lines inclined to one another…

Illustration used to find the center of a circle.

Center of a Circle

Illustration used to find the center of a circle.

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…

"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…

The illustration of constructing a circle or ellipse using isometric drawing. The inscribed circle is transferred to the top part of the cube by creating diagonal lines through the center and series of squares.

Isometric Drawing of Circle using Square

The illustration of constructing a circle or ellipse using isometric drawing. The inscribed circle is…

"Join AB and BC, bisect AB and BC by perpendiculars. Their intersection will be the center of the required circle." —French, 1911

Draw Circular Arc Through Three Given Points

"Join AB and BC, bisect AB and BC by perpendiculars. Their intersection will be the center of the required…

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…

"On horizontal center line mark off eight points 3/8" apart, beginning at right side of space." —French, 1911

Drawing Concentric Arcs with Compass and Lengthening Bar

"On horizontal center line mark off eight points 3/8" apart, beginning at right side of space." —French,…

"On horizontal center line mark off eleven points 1/4" apart, beginning at left side of space. Draw horizontal limiting lines (in pencil only) 1 1/2" above and below center line." —French, 1911

Drawing Concentric Arcs with Compass

"On horizontal center line mark off eleven points 1/4" apart, beginning at left side of space. Draw…

"Draw Horizontal line throuch center of space. On it mark off radii for six concentric circles 1/4" apart. In drawing concentric circles always draw the smallest first. The dotted circles are drawn in in pencil with long dashes, and inked as shown." —French, 1911

Drawing Concentric Circles with Compass

"Draw Horizontal line throuch center of space. On it mark off radii for six concentric circles 1/4"…

Development and top completion exercise problem of the cone by dividing the base into equal parts and creating an arc to revolve the sides of the plane.

Development Exercise of Cone

Development and top completion exercise problem of the cone by dividing the base into equal parts and…

An exercise problem to complete the top and develop, stretched out, image of the flange and hood cones by using series of cone development.

Development Exercise of Flange and Hood Cones

An exercise problem to complete the top and develop, stretched out, image of the flange and hood cones…

The cone is sliced by a circle in a plane perpendicular to the axis. This can be drawn without knowledge of equations from analytic geometry.

Conic Section Using Circle

The cone is sliced by a circle in a plane perpendicular to the axis. This can be drawn without knowledge…

The cone is sliced by a ellipse by making an angle within the plane. This can be drawn with knowing characteristics of each shape.

Conic Section Using Ellipse

The cone is sliced by a ellipse by making an angle within the plane. This can be drawn with knowing…

The cone is sliced by a hyperbola within a plane. The angle of the hyperbola will make a smaller angle than the other elements.

Conic Section Using Hyperbola

The cone is sliced by a hyperbola within a plane. The angle of the hyperbola will make a smaller angle…

Diagram showing how to construct a conic when given the focus and the auxiliary circle. If the focus is outside the circle, we get a hyperbola. If it's inside the circle, we get an ellipse. If the auxiliary circle is a straight line (radius is infinite), we get a parabola.

Construction of a Conic

Diagram showing how to construct a conic when given the focus and the auxiliary circle. If the focus…

Diagram showing how to construct a conic when given the focus and the auxiliary circle. The focus is on the left of the auxiliary circle, thus producing a very obtuse hyperbola.

Focus In Auxiliary Circle of Conic

Diagram showing how to construct a conic when given the focus and the auxiliary circle. The focus is…

Diagram showing how to construct a conic when given the focus and the auxiliary circle. As the focus moves inside the circle the ellipse broadens out until the focus reaches the center and becomes a circle.

Focus In Auxiliary Circle of Conic

Diagram showing how to construct a conic when given the focus and the auxiliary circle. As the focus…

Method to construct an equilateral triangle

Construct Equilateral Triangle

Method to construct an equilateral triangle

Method to construct an isosceles triangle

Construct Isosceles Triangle

Method to construct an isosceles triangle

Method to construct a scalene triangle

Construct Scalene Triangle

Method to construct a scalene triangle

A parabola can be constructed by using the parallelogram method of ellipses. —French, 1911

Constructing Parabola using Parallelogram

A parabola can be constructed by using the parallelogram method of ellipses. —French, 1911

An ellipsograph uses the trammel method to create ellipses.

Construction of Ellipse using Ellipsograph

An ellipsograph uses the trammel method to create ellipses.

Construction of Ellipse using Parallelogram

Create diameters with major, minor axes, or a pair of conjugate diameters. Construct a parallelogram,…

An ellipse can be constructed by pinning three pins and tying an inelastic in tightly around the pins.

Construction of Ellipse using Pin and String

An ellipse can be constructed by pinning three pins and tying an inelastic in tightly around the pins.

Trammel method is a construction of an ellipse using a strip of paper, thin cardboard or sheet celluloid.

Construction of Ellipse using Trammel Method

Trammel method is a construction of an ellipse using a strip of paper, thin cardboard or sheet celluloid.

Illustration of the construction used to bisect a given angle.

Construction of Bisecting a Given Angle

Illustration of the construction used to bisect a given angle.

Illustration of the construction used to bisect a given arc.

Construction of Bisecting a Given Arc

Illustration of the construction used to bisect a given arc.

Illustration of the construction used to bisect a given line.

Construction of Bisecting a Given Line

Illustration of the construction used to bisect a given line.

Illustration used to construct a circle when given two points that it passes through and a radius.

Construction of a Circle When Given Two Points and a Radius

Illustration used to construct a circle when given two points that it passes through and a radius.

Illustration of a triangle with its incircle and three excircles constructed.

Triangle With Circle Constructions

Illustration of a triangle with its incircle and three excircles constructed.

Illustration of the construction used to circumscribe a circle about a given triangle.

Construction to Circumscribe a Circle About a Triangle

Illustration of the construction used to circumscribe a circle about a given triangle.

Construction of a Common Tangent When Given Two Circles

Illustration used to construct a common tangent when given two circles.

Construction of Dividing Lines

A line which is divided into seven equal parts, shown by construction.