Question

Two circles of radii 3 cm and 2 cm are at a distance of 5 cm. Draw a transverse common tangent and measure its length.

Answer 1

Draw the circle $C1$ of radius $3cm$ with $A$ as centre. Let $AB=10cm$.

Draw circle $C2$ of radius $2cm$ with $B$ as centre.

Draw circle $C3$ of radius $5cm$ (sum of radii $C1$ and $C2$) with $A$

Bisect the line $AB$ to get its midpoint $M$. With $M$ as centre and $AM$ as radius, draw an arc to cut $C3$ at $X$. $BX$ is tangent to $C3$ at $X$.Join $XA$ to meet $C1$ at $P$

Draw a line from $B$ parallel to $APX$. Let this line cut $C2$ at $R$.

Draw a line from $P$ to $R$.

$PR$ is the transverse common tangent.

$PR=\sqrt{d^2-(r_1+r_2{)}^2}PR=\sqrt{(10{)}^2-(3+2{)}^2}=\sqrt{75}PR=8.66cm$