Coatbridge High School

Technology Technology Department Department

Gra

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G

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C

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Com

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Tangency

Tangency

2 Lines

A Curve Tangential to 2 Lines

Draw two arcs with the centre on the lines

Draw two lines parallel to the other lines & tangential to the curves

Where the two lines intersect is the centre of the arc which will touch both lines.

Final Result

Firm in Outlines

Finding Tangency Points

•Draw a line through the center of the arc and at 90º to the line.

•The tangency point is the point of intersection.

•Repeat for other point.

Tangency 2

2 Lines at an angle

Two lines at an angle

Find the CentreDraw a curve with the radius required from any point on the line.

Draw a line tangential to the curve and parallel to the first.Repeat this for the other line.

Draw the CurveUsing the point of intersection of the two red lines as your centre, draw in the curve.

Find the Tangency PointsTo find the exact point of tangency between the line and the curve, draw a line which is at 90º to the line and passes through the centre of the curve.

Repeat for the other line.

Mark the points with a small circle.

T2Firm in the curve and lines.

Tangency

2 Circles

Circle to Circle 1

R20

R30

R20

40

50

Circle to Circle 1

40

50

R20

R30

R20

40

50

Locate Centre of ArcUsing a compass set to 40 (20+20), from the centre of the small circle draw an arc.

Using a compass set to 50 (30+20), from the centre of the large circle draw an arc intersecting the previous one

Circle to Circle 1

40

50

R20

R30

R20

40

50

Using a compass set to 20, from the intersection of the arcs, draw the curve.

Draw a light line between the centres.

Where the lines cross indicate tangency points.

Tangency

2 Circles

Circle to Circle 2

100-20=80

100-30=70

R20

R100

100-20=80 100-30=70

R30

Locate Centre of Arc

Using a compass set to 80 (100-20), from the centre of the small circle draw an arc.

Using a compass set to 70 (100-30), from the centre of the large circle draw an arc intersecting the previous one

Circle to Circle 2

100-20=80

100-30=70

R20

R100

100-20=80 100-30=70

R30

Using a compass set to 100, from the intersection of the arcs, draw the curve.

Draw a light line between the centres.

Where the lines cross the outside of the circle indicate tangency points.