Transverse Common Tangents

The word tangent comes from the latin verb tangere, meaning to touch. Tangent lines touch a curve at a single point.

Scroll down to step through the instructions.

01. Given two circles, label their centers A and B and draw a line between these points. Circle A should represent the larger of the two circles.

02. Identify the point of intersection between circle A and line AB.

Draw an arc with this point at its center with a radius equal to circle B. Be sure that this arc crosses line AB on the outside of circle A.

03. Fix your rope or string at point A and extend it to point C. Rotate around point A to draw a circle.

04. Find the midpoint of line AB using the folding method and label it D.

Fix your rope or string at this point and extend it to point A. Rotate around the midpoint of line AB to draw a circle.

05. Identify the point of intersection between circle D and the larger circle about point A. Label this point E.

Draw a line that passes through points A and E.

06. Identify the point of intersection between line AE and the larger circle about A.

Perform the operations to find a perpendicular line at a given point to find the line perpendicular to line AE at this point.

07. Repeat steps 05 and 06 on the other half of the drawing.

08. You have drawn the direct common tangents of two circles!