## 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.

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.

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° 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 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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### Responses

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?
4 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
• WISEMAN
How to construct regular hexagon with distance across flat and corner?
3 years ago
• anya hunter
How to construct a hexagon with distance across corners?
3 years ago
• dahlak mebrahtu
How to draw a hexagon of flat and corner?
3 years ago
• jens
How to get 90mm across flat?
3 years ago
• Michelangelo
How to construct a octagon with diameter 82mm using across corners method?
3 years ago
• Nibs Whitfoot
How to draw a regular octagon across flats and corners?
3 years ago
• LEENA
How to draw octagon using set square?
3 years ago
• wilimar
Where is the distance across the flats of oactagon loacated?
3 years ago
• vernon
How to construct a regular hexagon 90 mm across flats?
3 years ago
• EIJA-RIITT
How to circumscribe a hexagon across corners from circle with a radius of 25mm?
3 years ago
• hiewan yemane
How to draw a circumscribed circle?
3 years ago
• fiyori
How to solve distance across coners in drawing and design?
2 years ago
• maximilian
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
How to construct regular hexagons 90mm across flats?
2 years ago
• MAY BOFFIN
How to give across flat?
2 years ago
• Primrose Gammidge
How to draw a regular octagon across flat?
2 years ago
• demsas
How construct an octagon across the flat?
2 years ago
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How to draw regular octagon across flat in technical drawing?
2 years ago
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How to construct a hexagon with 60° set square?
2 years ago
• yolanda
How To Construct A Regular Hexagon Across Flat Of 90mm?
2 years ago
• LUCA HIRSCH
How to draw a regular hexagon of 90mm by flat?
2 years ago
• sirja
Is the distance across flats equal to the diameter of the circle?
2 years ago
• michelle
How to construct an octagon given a distance across corner to be 60?
2 years ago
• christina
How to construct a regular polygon when a distance are line?
2 years ago
• simone
What does distance across flats and corners mean?
2 years ago
• aila palo
What is a polygon in drawing for engineering?
2 years ago
• miya
How to construct an octagon given the distance across corners?
2 years ago
• J
How to construct a regular hexagon given the distance across flats?
2 years ago
• Keke
How to draw an octagon wen distance across flat and corners are given?
2 years ago
• florian
What is the difference between distance across flats and corners?
2 years ago
How to draw an Octagon using distance across flats?
2 years ago
• randall
How to construct polygon on flat?
2 years ago
• jennifer
How to construct a spinner 150 length hole of 90 and 30mm across corner?
2 years ago
How to construct a regular octagon of 90 mm across flats?
2 years ago
• Annie
How to draw heptagon in 90mm distance?
2 years ago
• aapo
How to construct a regular Pentagon across flat?
2 years ago
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How to construct an octagon of a specified length across flat and also across corner?
2 years ago
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How to xraw an octagin when given the across flat dimemsion?
2 years ago
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How to construct a regular pentagon across the flats?
2 years ago
• theresa
How to construct a hexagon using a 60 set square when given a length?
2 years ago
• troy
What Are Different Ways Of Drawing Polycons Apart From Across The Flats&corners?
2 years ago
• mimosa
How To Draw Polycons Using Across Flats?
2 years ago
• FELIX
How to construct an octagon using the general method?
2 years ago
• ludovico endrizzi
How to draw octagon in engineering drawing?
2 years ago
How to construct a regular octagon given the distance across flats?
2 years ago
• NIKLAS NIINIMAA
How to construct an hexagon given the distance acros corners?
2 years ago
• Kidane
How to draw a regular octagon in engineering drawing?
2 years ago
• May Brown
How to draw a hexagon given the distance of flats?
2 years ago
• zufan
How to construct regular octagon in geometrical construction in engineering graphics and design?
2 years ago
• hildibrand
How To Get Across Flat Hexagonal?
2 years ago
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How ti draw a hexagon technical drawing?
2 years ago
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How todraw regular polygon octagon side = 45 semicircular method?
1 year ago
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How to construct a regular pentAgon circumscribed in a circle when across flat given?
1 year ago
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What is polygon and how to construct it in engineering drawing?
1 year ago
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How to construct octagon by semi circle?
1 year ago
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How to make octagon engineering?
1 year ago
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How to construct an octagon using 45 degree set square when given the length of side?
1 year ago
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How to construct a regular hexagon in engineering drawing?
1 year ago
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What does across the corners mean graphics?
4 months ago
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How to draw a pentagon around flat and around corners engineering drawing?
3 months ago
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How to contruct a hexagon using flat corner method?
2 months ago
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How to construct a regular hexagon 90mm across flats?
2 months ago
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How to draw a regular nonagon with a diameter of 90mm?
2 months ago
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How to construct a nonagon given the distance across corners?
2 months ago
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How to construct a regular nonagon across coners?
1 month ago
• rosamunda
HOW TO DRAW AN OCTAGON USING THE SEMICIRCLE METHOD?
28 days ago
• Hyiab
How to construct a regular octagon using one circle?
27 days ago