Draw a Tangent Between Two Circles
Tangency
Definition
A tangent to a circumvolve it a ttraight lino which touches the circle at 1 point.
Every curve always fatigued could take tangent« drawn to it but this chapter is concerned only with tangents to circles. These accept wide applications in Applied science Drawing since the outlines of most technology details are made up of straight lines and arcs. Wherever a directly line meets an arc, a tangent meets a circumvolve.
Constructions
To draw a tangent to e circle from any point on the circumference (Fig. 5/1 )
one. Depict the radius of the circumvolve.
2. At whatsoever point on the circumference of a circle, the tangent and the radius are perpendicular to each other. Thus, the tangent is constitute 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 bending (Fig. five/2). This fact is made use of in many tangent constructions.
To construct a tangent from a indicate P to a circle, heart O (Fig. five/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 circumvolve from P but only one has been shown for clerity.
To conetruct a common tangent to ii equal circlea (Fig. six/4)
1. Join the centres of the two circles.
2. From each middle, con struct lines at 90* to the eye line. The intersection of these perpendiculars with the circles gives the points of tangency.
This tangent is often descnbed at the common extenor tangent.
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To construct the mutual interior (or transverse or cantankerous) tangent to two equal circles, centres O
ane. Join the centres 0 0,.
three. Bisect OA In B and draw a semi-circle, radius BA to cut the circle in C.
t respectively (Fig v/half dozen)
1. Bring together the centres 00,.
ii. Bisect 0 O, in A and draw e semi-circle, radius AO.
iii. Draw a circle, center 0, radius R-r. to cut the semi-
t respectively (Fig v/6)
1. Join the centres 00,.
2. Bisect 0 O, in A and draw e semi-circle, radius AO.
iii. Draw a circle, eye 0, radius R-r. to cutting the semi-
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To construct the mutual internal tangent between two unequal circle«, centres O and O, and radii R andr respectively (Fig. five/vii)
1. Join the centres 00,.
ii. Bifurcate 0 0, in A and draw a semi-circle, radius OA.
3. Drew a circle, middle 0. radius R + r. to cutting the semicircle in B.
iv. Bring together 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 oftentimes talk of radii or curves meeting each other tengentially. We mean, of grade, that the curves meet smoothly and with no modify of shape or bumps. This topic, the blending of lines and curves, is discussed in Chapter viii.
ii Fig. 2 shows a heart finder, or centre square in position on a 75 mm diameter bar.
Oraw, full tin can. the shape of the centre finder and the piece of round bar. Evidence 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 i
(a) Draw the former, full sue. showing in full the structure for obtaining the tangent joining the two arcs
(b) Determine, without calculation, the centres of the four as spaced holes to be bored in the positions indicated in the figure.
Middlesex Regional Examining Lath
| rV | ||
| si | ||
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| 130 |
01 MENS IONS IN mm fig. 1
01 MENS IONS IN mm fig. 1
(b) the points of contact and the heart for the 44 mm rad at B;
(c) the points of contact and the heart for the 50 mm rad at C.
South-Cast Regional examinations Board (See Ch. 8 for information non in Ch Due south)
Dimensions IN ■
Dimensions IN ■
3. Rg. three shows the outline of two pullsy wheels connected by a chugalug of negligible thickness. To a scalo of one/10 describe the figure showing the structure necessary to obtain the points of contact of the belt and pulleys.
Middlesex Regional Examining Board
four. (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 bespeak B
(3) Construct a tangent from the indicate P to bear on the circumvolve on the minor arc of the chord Ac.
Southern Regional Examining Board (Run into Ch. 4 for information not in Ch. 5)
5. Fig. five shows a metal blank. Draw the blank, full size, showing clearly the constructions for obtaining the tangents joining the arcs.
-
- continued by a taut chugalug. Draw the effigy, total size, showing clearly the constructions for obtaining the points of contact of the belt and pulleys
7. Fig. vii shows the outline of a metal blank. Draw the bare, full size, showing clearly the constructions for finding exact positions of the tangents joining the arcs.
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OIMCNSIOH3 IN mm '
OIMCNSIOH3 IN mm '
8 A segment of a circumvolve 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 Schoolhouse Examinations (See Ch. 2 and Ch. 4 for information non in Ch. five)
9. A and B are 2 points 100 mm apart With B as center depict a circle 75 mm diameter. From A depict 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 out and state the lengths CD and Advertizement. also bending CDA Articulation Matriculation Board
10. Fig. viii shows two circles, A and 8. and a mutual external tangent and a common internal tangent. Construct (e) the given circles and tangents and (b) the smaller circle which is tangential to circumvolve B and the two given tangents.
Mensurate and state the distance betwixt the centres of the constructed circle and circle A. Associated Examining Boa/d (Come across Ch. 4 for information not in Ch. 5)
Continue reading hither: Oblique projection
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