Geometrical constructions and tangency

Students will often experience difficulty in handling problems involving two and three dimensional geometrical constructions. The examples in Chapters 9 to 13 are included in order to provide a background in solving engineering problems connected with lines, planes and space. The separate chapters are grouped around applications having similar principles.

Copying a selection of these examples on the drawing board or on CAD equipment will certainly enable the reader to gain confidence. It will assist them to visualize and position the lines in space which form each part of a view, or the boundary, of a three dimensional object. It is a necessary part of draughtsmanship to be able to justify every line and dimension which appears on a drawing correctly.

Many software programs will offer facilities to perform a range of constructions, for example tangents, ellipses and irregular curves. Use these features where possible in the examples which follow.

Assume all basic dimensions where applicable.

To bisect a given angle AOB (Fig. 9.1)

1 With centre O, draw an arc to cut OA at C and OB at D.

2 With centres C and D, draw equal radii to intersect at E.

3 Line OE bisects angle AOB.

To bisect a given straight line AB (Fig. 9.2)

1 With centre A and radius greater than half AB, describe an arc.

2 Repeat with the same radius from B, the arcs intersecting at C and D.

3 Join C to D and this line will be perpendicular to and bisect AB.

\C

A

/

(d

1 With centre A and radius greater than half AB, describe an arc.

2 Repeat with the same radius from B, the arcs intersecting at C and D.

3 Join C to D to bisect the arc AB.

To find the centre of a given arc AB (Fig. 9.4)

1 Draw two chords, AC and BD.

2 Bisect AC and BD as shown; the bisectors will intersect at E.

3 The centre of the arc is point E.

Horse Head Drawing With Name

Circle radius

To inscribe a circle in a given triangle ABC (Fig. 9.5)

1 Bisect any two of the angles as shown so that the bisectors intersect at D.

2 The centre of the inscribed circle is point D.

To circumscribe a circle around triangle ABC (Fig. 9.6)

1 Bisect any two of the sides of the triangle as shown, so that the bisectors intersect at D.

2 The centre of the circumscribing circle is point D.

To draw a hexagon, given the distance across the corners

1 Draw vertical and horizontal centre lines and a circle with a diameter equal to the given distance.

2 Step off the radius around the circle to give six equally spaced points, and join the points to give the required hexagon.

Circle radius

Circle Centre Engineering

1 Draw vertical and horizontal centre lines and a circle with a diameter equal to the given distance.

2 With a 60° set-square, draw points on the circumference 60° apart.

3 Connect these six points by straight lines to give the required hexagon.

.- 60° set-square

\ 60°

Tee-square

To draw a hexagon, given the distance across the flats (Fig. 9.8)

1 Draw vertical and horizontal centre lines and a circle with a diameter equal to the given distance.

2 Use a 60° set-square and tee-square as shown, to give the six sides.

60° set-square

60° set-square

Tee-square

To draw a regular octagon, given the distance across corners (Fig. 9.9)

Repeat the instructions in Fig. 9.7(b) but use a 45° setsquare, then connect the eight points to give the required octagon.

To draw a regular octagon, given the distance across the flats (Fig. 9.10)

Repeat the instructions in Fig. 9.8 but use a 45° setsquare to give the required octagon.

45° set-square

45° set-square

Across The Flats Hexagon

To draw a regular polygon, given the length of the sides (Fig. 9.11)

Note that a regular polygon is defined as a plane figure which is bounded by straight lines of equal length and which contains angles of equal size. Assume the number of sides is seven in this example.

1 Draw the given length of one side AB, and with radius AB describe a semi-circle.

2 Divide the semi-circle into seven equal angles, using a protractor, and through the second division from the left join line A2.

3 Draw radial lines from A through points 3, 4, 5, and 6.

4 With radius AB and centre on point 2, describe an arc to meet the extension of line A3, shown here as point F.

Repeat with radius AB and centre F to meet the extension of line A4 at E. Connect the points as shown, to complete the required polygon.

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  • bildad grubb
    How to draw an octagon of distance asross corners?
    8 years ago
  • darnell
    How to draw an octagon across flats?
    4 years ago
  • alfrida
    How to construct a octagon across flats?
    4 years ago
  • laurence
    How to draw regular hexagon using set square?
    3 years ago
  • dorothy
    How to construct polygon using tee square and set square given distance across corners?
    3 years ago
  • kane
    How to draw a hexagon given a distance across flat?
    3 years ago
  • melissa
    How to draw a regular octagon across a distance?
    3 years ago
  • rorimac
    What is an across flat polygon?
    3 years ago
  • selamawit
    How to use set squares to draw hexagon across flat and corners?
    3 years ago
  • heikki h
    How to use set squares to draw an octagon across flat and corners?
    3 years ago
  • Giordana
    How to place my set squares to draw an octagon across flat?
    3 years ago
  • makda
    How to place my set squares to draw an hexagon across flat?
    3 years ago
  • robel
    How to construct hexagon when givena distant across the flats A/F 60?
    3 years ago
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    How to construct regular hexagon with distance across flat and corner?
    2 years ago
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    How to construct a hexagon with distance across corners?
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    How to draw a hexagon of flat and corner?
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    How to get 90mm across flat?
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    How to draw a regular octagon across flats and corners?
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    How to draw octagon using set square?
    2 years ago
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    Where is the distance across the flats of oactagon loacated?
    2 years ago
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    How to construct a regular hexagon 90 mm across flats?
    2 years ago
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    How to circumscribe a hexagon across corners from circle with a radius of 25mm?
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    How to draw a circumscribed circle?
    2 years ago
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    How to solve distance across coners in drawing and design?
    2 years ago
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    How to construct polygons given distance across corners?
    2 years ago
  • caoimhe
    Which engineering drawing provides answers to the geometrical constructions?
    2 years ago
  • Cassidy
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    2 years ago
  • MAY BOFFIN
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    2 years ago
  • Primrose Gammidge
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    2 years ago
  • demsas
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    2 years ago
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    2 years ago
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    How To Construct A Regular Hexagon Across Flat Of 90mm?
    2 years ago
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    How to draw a regular hexagon of 90mm by flat?
    2 years ago
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    Is the distance across flats equal to the diameter of the circle?
    2 years ago
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    2 years ago
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    2 years ago
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    2 years ago
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    2 years ago
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    How to construct an octagon given the distance across corners?
    2 years ago
  • J
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    2 years ago
  • Keke
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    2 years ago
  • florian
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    2 years ago
  • jade
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    2 years ago
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    2 years ago
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    2 years ago
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    How to construct a regular octagon of 90 mm across flats?
    2 years ago
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    2 years ago
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    How to construct a regular Pentagon across flat?
    2 years ago
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    How to xraw an octagin when given the across flat dimemsion?
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    What Are Different Ways Of Drawing Polycons Apart From Across The Flats&corners?
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    How To Draw Polycons Using Across Flats?
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