Question

Draw a transverse common tangent to two circles of radii $4cm$ and $2cm$ whose centres are $9cm$ apart. Measure the length of the tangent.

Answer 1

Measuring the length of tangent $AR$ using ruler we get $6.7cm$.

Alternate solution:

We know that $\Delta OAT\sim \Delta PRT$

Therefore,

$\frac{OA}{PR}=\frac{OT}{PT}=\frac{4}{2}=\frac{2}{1}$

Also $OP=9cm$

$\Rightarrow OT=6cm,PT=3cm$

$\therefore AR=\sqrt{6^2-4^2}+\sqrt{3^2-2^2}=6.7cm$