Being able to construct tangents to circles accurately is an important part of your SEC Graphical Communication studies. These skills are not only tested in exams but are also widely used in design, engineering, and technical drawing. Practising these constructions helps improve precision and spatial awareness in your drawings.
Circles can either touch other circles or lines, which we call tangents. When two or more circles touch, we add or subtract their radii to construct their special point of tangencies. When circles touch tangents, we have special constructions as well to use so that we find the exact point of tangency. A point of tangency is always perpendicular to the circle. A line from the point of tangency to the centre of the circle produces a normal. Normals and tangents are also perpendicular to each other.
Constructing tangents to circles is a key topic in graphical communication and engineering drawing. A tangent is a straight line that touches a circle at exactly one point, without crossing it. These constructions are essential when drawing circular components, linkages, and transitions in technical diagrams. Using a compass and ruler, students can learn to construct tangents from a point to a circle, as well as tangents between two circles of equal or unequal size.
This construction is used when a point lies outside a circle and you need to draw one or two straight lines that touch the circle exactly once.
Key Steps: Locate the midpoint between the external point and the circle’s center, draw a semicircle, then use intersection points to find the tangent lines.
When two circles of the same diameter are placed apart, tangents can be drawn to touch both circles either on the outer or inner sides. These are known as external tangents and internal tangents.
Key Steps: Connect the centers, construct a line perpendicular to that at the correct offset (equal to the radius), and project the tangent lines using compass arcs.
When the two circles have different radii, the method changes slightly. You need to account for the difference in diameter when transferring distances with the compass.
Key Steps: Subtract or add the radii when drawing auxiliary circles or arcs, and use intersecting arcs or bisectors to locate tangent points accurately.
