Question

Draw direct common tangents to two circles of radii 5 cm and 3 cm having their centres 5 cm apart.

Answer 1

• Draw a line segment $AB=5cm$. Draw circle $C1$ with radius $5cm$ and centre as $A$. Draw circle $C2$ with radius $3cm$ and centre $B$
• Draw circle $C3$ with radius $(R_1-R_2=5-3=2cm$ and centre $A$. $B$ is the external point to circle $C3$. Draw perpendicular bisector of $AB$ and mark its midpoint $M$
• With $M$ as centre and $AM$ as radius construct a circle $C4$
• $C4$ cuts $C3$ at two points $E$ and $F$. Join $AE$ and $AF$
• Extend $AE$ to meet $C1$ at $P$ and $AF$ to meet $C1$ at $Q$
• Draw $BR\parallel AP$ and $BS\parallel AS$
• Join $PR$ and $QS$. $PR$ and $QS$ are required tangents.