## Tangency

Definition

A tangent to a circle it a ttraight lino which touches the circle at one point.

Every curve ever drawn could have tangent« drawn to it but this chapter is concerned only with tangents to circles. These have wide applications in Engineering Drawing since the outlines of most engineering details are made up of straight lines and arcs. Wherever a straight line meets an arc, a tangent meets a circle.

Constructions

To draw a tangent to e circle from any point on the circumference (Fig. 5/1 )

### 1. Draw the radius of the circle.

2. At any point on the circumference of a circle, the tangent and the radius are perpendicular to each other. Thus, the tangent is found by constructing en angle of 90* from the point where the radius crosses the circumference.

A base geometric theorem is that the angle in a semicircle is a right angle (Fig. 5/2). This fact is made use of in many tangent constructions.

To construct a tangent from a point P to a circle, centre O (Fig. 5/3)

2. Erect a semi -circle on 0 P to cut the circle in A.

PA produced is the required tangent (OA is the radius and is perpendicular to PA since rt is the angle in a semicircle). There are. of course, two tangents to the circle from P but only one has been shown for clerity. To conetruct a common tangent to two equal circlea (Fig. 6/4)

### 1. Join the centres of the two circles.

2. From each centre, con struct lines at 90* to the centre line. The intersection of these perpendiculars with the circles gives the points of tangency.

This tangent is often descnbed at the common extenor tangent. Urheberrechtlich gesch

To construct the common interior (or transverse or cross) tangent to two equal circles, centres O

3. Bisect OA In B and draw a semi-circle, radius BA to cut the circle in C. t respectively (Fig 5/6)

1. Join the centres 00,.

2. Bisect 0 O, in A and draw e semi-circle, radius AO.

3. Draw a circle, centre 0, radius R-r. to cut the semi-

t respectively (Fig 5/6)

1. Join the centres 00,.

2. Bisect 0 O, in A and draw e semi-circle, radius AO.

3. Draw a circle, centre 0, radius R-r. to cut the semi- rechtlich geschützte

To construct the common internal tangent between two unequal circle«, centres O and O, and radii R andr respectively (Fig. 5/7)

1. Join the centres 00,.

2. Bisect 0 0, in A and draw a semi-circle, radius OA.

3. Drew a circle, centre 0. radius R + r. to cut the semicircle in B.

4. Join OB. This cuts the larger circle in C.

5. Draw O.D parallel to OB. CO is the required tangent

A tangent is. by definition, a straight line. However, we do often talk of radii or curves meeting each other tengentially. We mean, of course, that the curves meet smoothly and with no change of shape or bumps. This topic, the blending of lines and curves, is discussed in Chapter 8. 2 Fig. 2 shows a centre finder, or centre square in position on a 75 mm diameter bar.

Oraw, full tin. the shape of the centre finder and the piece of round bar. Show clearly the constructions

2 Fig. 2 shows a centre finder, or centre square in position on a 75 mm diameter bar.

Oraw, full tin. the shape of the centre finder and the piece of round bar. Show clearly the constructions

Exercises 5 (All questions originally set in Imperial units) 1. A former in a jig for bending metal is shown in Fig 1

(a) Draw the former, full sue. showing in full the construction for obtaining the tangent joining the two arcs

(b) Determine, without calculation, the centres of the four equally spaced holes to be bored in the positions indicated in the figure.

Middlesex Regional Examining Board

 rV si 1 130

01 MENS IONS IN mm fig. 1

01 MENS IONS IN mm fig. 1

(b) the points of contact and the centre for the 44 mm rad at B;

(c) the points of contact and the centre for the 50 mm rad at C.

South-Cast Regional examinations Board (See Ch. 8 for information not in Ch S) Dimensions IN ■

Dimensions IN ■

3. Rg. 3 shows the outline of two pullsy wheels connected by a belt of negligible thickness. To a scalo of 1/10 draw the figure showing the construction necessary to obtain the points of contact of the belt and pulleys.

Middlesex Regional Examining Board

4. (1 ) Draw the figure ABCP shown in Fig. 4 and construct a circle, centre 0. to pass through the points A. 8 and C.

(2) Construct a tangent to this circle touching the circle at point B

(3) Construct a tangent from the point P to touch the circle on the minor arc of the chord AC.

Southern Regional Examining Board (See Ch. 4 for information not in Ch. 5)

 /V»' af\c i

5. Fig. 5 shows a metal blank. Draw the blank, full size, showing clearly the constructions for obtaining the tangents joining the arcs. connected by a taut belt. Draw the figure, full size, showing clearly the constructions for obtaining the points of contact of the belt and pulleys

7. Fig. 7 shows the outline of a metal blank. Draw the blank, full size, showing clearly the constructions for finding exact positions of the tangents joining the arcs.

 _ S' _ —1 ¡.«L OIMCNSIOH3 IN mm ' 8 A segment of a circle stands on a chord AB which measures 50 mm The angle in the segment is 55°. Draw the segment. Produce the chord AB to C making BC 56 mm long. From C construct a tangent to the arc of the segment. University of London School Examinations (See Ch. 2 and Ch. 4 for information not in Ch. 5) 9. A and B are two points 100 mm apart With B as centre draw a circle 75 mm diameter. From A draw two lines AC and AD which are tangential to the circle AC « 150 mm. From C construct another tangent to the circle to form a triangle ACD. Measure and state the lengths CD and AD. also angle CDA Joint Matriculation Board 10. Fig. 8 shows two circles, A and 8. and a common external tangent and a common internal tangent. Construct (e) the given circles and tangents and (b) the smaller circle which is tangential to circle B and the two given tangents. Measure and state the distance between the centres of the constructed circle and circle A. Associated Examining Boa/d (See Ch. 4 for information not in Ch. 5) 0 0 ## Pencil Drawing Beginners Guide

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### Responses

• Eliano
How draw transverse tangent to two unequal circles apart?
8 years ago
• lioba
How to get angle of joint on a semi circle?
8 years ago
• Efrem
How to construct a belt which form cross or transverse tangents to wheeles?
8 years ago
• John
How to construst a belt which will form cross or transverse tangents to wheels?
8 years ago
• Annika Helminen
How to draw a pulley between three circles that form tangents?
8 years ago
• Lily-rose
Do common internal tangents bisect each other?
8 years ago
• Andwise
How to construct an internal tangent in technical drawing?
8 years ago
• THEOBALD
How to draw two circles connect at required point?
8 years ago
• taija
How to draw the tangents to two circles in engineer drawing?
7 years ago
• Lucas
How do i construct a Sshaped curve that meets at a point of tangency to connect two lines?
7 years ago
• Richard
HOW MANY DIMENSIONDS ARE REQUIRED FOR TANGENT RADIUS ON A DRAWING?
7 years ago
• andrea
HOW TO DRAW A LINE BETWEEN TWO TANGENTS OF A CIRCLE?
7 years ago
• Demi
How to draw former full size showing in full construction for obtaining a tangent joining two arcs.?
4 years ago
• baldassarre
How to draw the centre finder and the piece of rouod bar?
3 years ago
• marjo
How to construst tangency?
3 years ago
• moro smallburrow
How to draw interior tangency of two circles?
3 years ago
• Kaiden
How arc appear when construct internal tangent of two equal circle?
3 years ago
• caelan
How to draw a common internal tangent to two unequal circles?
3 years ago
• petra shuster
How to draw a common internal tangent to two equal circle?
3 years ago
• ted
How to draw a tangent in two equal circles pictures?
3 years ago
How to show points of contact btwn three wheels of a pulley and the belt in engineering drawing?
3 years ago
• barbara
How to draw common internal tangents of two circles?
3 years ago
• Aliisa
How to draw internal tangent to two equal circles?
3 years ago
• Hallie McLean
How to draw external tangents to two circles of unequal diameters?
3 years ago
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How to construct a 3 pulley technical drawing?
2 years ago
• matta
How to construct an internal tangent between two unequal circles technical drawing?
2 years ago
How to construct an external tangent between two unequal circles?
2 years ago
• iggi
How to construct an internal tangent to two equal circles?
2 years ago
• RALPH
How to construct three pulley wheels connected by a taut belt?
2 years ago
• heike
How to draw a tagent to meet two circles?
2 years ago
• terhi
How to calculate the length of a belt in transverse tangents?
2 years ago
• FIKRU
How to drawn an external line tangent on two circle?
2 years ago
• quintilia
How to draw internal tangent to two unequal circle apart?
2 years ago
• Natsnet
How construct a common interior tangent to two unequal circle?
2 years ago
• myley
How to draw an exterior tangent to two circles?
2 years ago
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How to draw a cross belt between two pulleys?
2 years ago
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How to draw a line tangent to 2 circles in board drawing?
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How to draw a machine belt showing all tangent point?
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How to draw a tangent to two circles pencil?
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How to drawinternal arc in tangency?
2 years ago
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HOW TO CONSTRUCT A TANGENT OF AN ARC WITH UNEQUAL CIRCLE RADIUS ZX?
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How to draw toilet seat using tangency?
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• EMERY
How to draw a tangent to touch a circle?
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• Ensio Sandell
How to draw a common external tangent to two unequal circle?
2 years ago
• segan asfaha
How to draw interal tangent of two unqual circle?
2 years ago
• martin
How to construct internal tangent to two unequal circle?
2 years ago
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How to draw direct belt tangency in engine drawing?
2 years ago
• zach
How to draw tangential curve in tech drawing?
2 years ago
• prima
When drawing. A tangent is it necesary. To outline the circles?
1 year ago
• BONACATA
How to draw internal tangent given two diameters spacsd 110mm?
1 year ago
• pandora
How to construct internal and external arcs on two circles?
1 year ago
• brunilde
How to blend three unequal circles?
1 year ago
• mentha
How to construct an external tangent to two unequal circles Geometric drawing?
1 year ago
• annabel
What it means by to draw an internal tangent to two equal circle?
1 year ago
• leeann
How to draw a tangent of a circle with 3 pulley find d arc?
11 months ago
• venerando
How to construct external tangent to two equal circles?
11 months ago
• RON
How to draw in tangents in unequal circle?
11 months ago
• Samantha
How to a cross tangent between two equal circles?
9 months ago