Question

Construct two circles of radii 2.5 cm and 3.5 cm whose centres are 8 cm apart. Construct a transverse common tangent. Measure its length and verify by calculation.

Answer 1

Draw a line segment $AB=8cm$

Draw the circle $C1$ of radius $3.5cm$ with $A$ as centre.

Draw circle $C2$ of radius $2.5cm$ with $B$ as centre.

Draw circle $C3$ of radius $6cm$ (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

$d^2=(PR{)}^2-(r_1+r_2{)}^{2}d=\sqrt{8^2-6^2}d=5.292cm$