Geometric Drawings 4 - Tangent Arc Connections

In our Technical Drawing Lessons section, this publication’s topic will be tangent arc connections (blending with arcs) in technical drawing. Connecting the arms of a right angle with an arc. Connecting the arms of an acute angle with an arc. Connecting the arms of an obtuse angle with an arc. Connecting a point outside a circle to the circle with an arc. Connecting a circle to a line AB outside it with an arc. We’ll look at how to blend two circles with a concave arc, and how to blend two circles with a convex arc.

Tangent Arc Connections in Technical Drawing

Connecting the Arms of a Right Angle with an Arc

Draw the right angle.
Draw lines parallel to the angle’s arms, at a distance of R.
Find where the parallel lines intersect, at points A and B.
Then open the compass to R, place its point at M, and connect A to B with an arc of radius R.

Connecting the Arms of an Acute Angle with an Arc

Draw the acute angle.
Draw lines parallel to the angle’s arms, at a distance of R.
From the point M we find, drop perpendiculars to the angle’s arms.
Then open the compass to R, place its point at M, and connect A to B with an arc of radius R.

Connecting the Arms of an Obtuse Angle with an Arc

Draw the arms of the obtuse angle.
Draw lines parallel to the angle’s arms, at a distance of R.
From the point M we find, drop perpendiculars to the angle’s arms.
Then open the compass to R, place its point at M, and connect A to B with an arc of radius R.

Connecting a Circle to a Point Outside It with an Arc

tangent arc connections in technical drawing

Draw the circle of radius R1. Opening the compass to R1 + R from the circle’s center, draw an arc.
Then, drawing an arc of radius R from point A, find the center point M.
Connect center M to the circle’s center O to find point B.
Placing the compass point at center M, connect an arc of radius R passing through A, tangent to the circle at B.

Connecting a Circle to a Line AB Outside It with an Arc

Draw a circle of radius R.
Take a line AB outside the circle.
Draw a line parallel to AB, at a distance of R1.
Placing the compass point at center O, find point M with an arc of radius R+R1.
Connect M to center O and extend the line.
Placing the compass point at center M, connect tangent points D and C.

Blending Two Circles with a Concave Arc

1- Draw the axes centered on M1 and M2.
2- Draw circles of radius R1 and R2.
3- Opening the compass to R1+R, draw an arc centered on M1; opening it to R2+R, draw an arc centered on M2.
4- Mark point A.

5- Connect the point A we found to points M1 and M2.
6- Mark arms B and C.
7- Open the compass to R, place its point at A, and blend the tangent arms B and C together with a concave arc.

Blending Two Circles with a Convex Arc

1- Draw axes M1, M2.
2- Draw circles of radius R1 and R2.
3- Opening the compass to R – R1, draw an arc centered on M1; opening it to R – R2, draw an arc centered on M2. 4- Mark point A.

5- Extend lines from the point A we found through centers M1 and M2 to mark points B and C.
6- Place the compass point at A and blend the arms B and C together with a convex arc of radius R.

Drawing a Tangent from a Point Outside a Circle

1- Connect points M and S.
2- Find the midpoint P of line MS.
3- Open the compass to PM, draw an arc, and find point R.
4- The line passing through points R and S is tangent to the circle.

Drawing an Internal Tangent Between Two Circles

1- Draw a circle of radius R1+R2 centered on M1.
2- Find the midpoint O of line M1M2.
3- Placing the compass point at O, connect M1 and M2 with an arc to find point A.
4- Connect A to M1 to find tangent point B.
5- Connect A to M2, and from M2

drop a perpendicular from A to the line M2 to find tangent point C.
The line passing through points B and C will be tangent to circles R1 and R2.

Drawing an External Tangent Between Two Circles

1- Draw a circle of radius R1-R2 centered on M1.
2- Find the midpoint O of line M1M2.
3- Placing the compass point at O, connect M1 and M2 with an arc to find point A.
4- Connect M1 to A and extend the line to find tangent point B.

5- Connect A and M2. From M2, drop a perpendicular from A to the line M2 to find tangent point C.
6- The line passing through points B and C will be tangent to circles R1 and R2.