Question

Draw two direct common tangents to two circles of radii $4cm$ and $2cm$ whose centres are $8cm$ apart. Measure the length of the tangents.

Answer 1

$d=8cm,R=4cmr=2$
$R-r=4-2=2cm$
Drawing circles $C_1,C_2$ with radius $R$ and $r$ and a circle $C_3$ concentric to $C_1$ with radius $R-r$.

Construct the perpendicular bisector of $AB$ and mark the midpoint as $M$. Draw a circle with centre $M$ and $AM$ as the radius and mark the intersection points with $C_3$ as $K$ and $L$. Join $B-K$ and $B-L$ which are the tangents to the circle $C_3$

Draw parallel lines to $BK$ and $BL$ at a distance of $R-r$ and name them as $PQ$ and $RS$. $PQ$ and $RS$ are the direct common tangents to circles $C_1$ and $C_2$.
Measuring and writing the length of tangents $PQ=RS$
$(PQ=RS=7.8cm)$