Question

Construct two circles of radii 4 cm and 2 cm whose centres are 8 cm apart. Construct a transverse common tangent. Measure and write its length.

Answer 1

Construct $2$ circles centred at $O$ and $O^{\prime }$ at a distance of $8$ cm.

Circle $O$ has radius $2$ cm. $O^{\prime }$ has radius $4$ cm.

Make another circle with radius $2+4=6cm$ centred on the bigger circle.

Make a semicircle with O and O' being two end points of diameter. Let it cut the largest circle at $N$.

Join $O^{\prime }N$ and make a line parallel to $O^{\prime }N$ passing through $O$. Let it cut the circle at $B$.

Name the point where $O^{\prime }N$ cuts the $4$cm circle as $B$.

$AB$ is the required tangent.

On measuring, it comes out to be $5.3$ cm.