Question

Construct a transverse common tangent to two circles of radii 4 cm and 3 cm whose centres are 10 cm apart. Measure and verify by calculation.

Answer 1

Draw a line segment $AB=10cm$

Draw the circle $C1$ of radius $4cm$ with $A$ as centre.

Draw circle $C2$ of radius $3cm$ with $B$ as centre.

Draw circle $C3$ of radius $7cm$ (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.

$d^2=(PR{)}^2-(r_1+r_2{)}^{2}d=\sqrt{(10{)}^2-7^2}=\sqrt{51}d=7.14cm$