In old style math, a span of a circle or circle is any of the line fragments from its middle to its edge, and in more current utilization, it is additionally their length.

In math, the circumference is the edge of a circle or oval.

A digression (tangent) to a circle is a straight line which contacts the circle at just one point.

A perpendicular bisector of a line section is a line fragment opposite to and going through the midpoint of (left figure).

Steps for constructions:

1. First draw a line $AB=6cm$.

2. At A, draw a circle of radius$3cm$.

3. At B, draw a circle of radius$2cm$.

4. At A, draw a third circle concentric to the bigger circle and radius,

$=3.5-2.5=1cm$

5. Then draw a perpendicular bisector of AB, assume H be the mid-point of AB.

6. Consider ‘H’ as center and AH as radii, draw a fourth circle.

7. Mark as G and I where the third and fourth circles intersect each other.

8. Now, join AG and AI and external line to meet the bigger circle at E and C.

9. Then join BG and BI.

10. On BG and BI, at F and D draw perpendicular to meet the smaller circle.

111. Now join EF and CD they will be the tangents.

Now we have to prove that, both direct common tangents to the circle are equal in length.

Since, $GE||FB$ and $CI||BD$,

So, $EF=GB$and $CD=BI$,

Now, consider the $\vartriangle ABG$ and$\vartriangle ABI$,

Then,$BG=BI$ … [tangents to a circle from same point]

Hence it is clear that, $EF=CD$