2. Coatbridge High School Tangency

3. 2 Lines

4. 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.

5. Final Result Firm in Outlines

6. 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.

7. Tangency 2 2 Lines at an angle

8. Two lines at an angle

9. Find the Centre Draw 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.

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

11. Find the Tangency Points To 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.

12. T2 Firm in the curve and lines.

13. Tangency 2 Circles

14. Circle to Circle 1 R20 R30 R 2 0 4 0 5 0

15. 4 0 5 0 Locate Centre of Arc Using 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

16. Circle to Circle 1 4 0 5 0 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.

17. Tangency 2 Circles

18. Circle to Circle 2 1 0 0 - 2 0 = 8 0 1 0 0 - 3 0 = 7 0 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

19. Circle to Circle 2 1 0 0 - 2 0 = 8 0 1 0 0 - 3 0 = 7 0 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.