Question

Construct direct common tangents to two circles of radii $4cm$ and $2cm$ whose centres are $9cm$ apart from their centres. Measure their length and write the length of direct common tangents.

Answer 1

1. Draw two circles with radii $4cm$ and $2cm$ having the centre $O$ and $A$ respectively, so that the centres are $9cm$ apart from each other.

2. Draw a third circle concentric with the first circle with centre $O$ and radius $4-2=2cm$.

3. Join $O-A$. Draw perpendicular bisector of $OA$. With one end of the compass at the midpoint of $OA$ and other end at $A$, draw arcs on the third circle.

4. Join $A$ to the intersection of the arcs with the circle. Now draw parallel lines to these tangents at a distance of $4-2=2cm$ away from the centre $O$.

$CS$ and $DT$ are the required tangents.

Measure their lengths which come out to be nearly $8.8cm$.