Draw two concentric circles of radii $3\, cm$ and $5\, cm$. Taking a point on the outer circle,construct a pair of tangents to the other circle. Measure the length of a tangent and verify it by actual calculation.

(N/A) Given: Two concentric circles with centre $O$ and radii $3\, cm$ and $5\, cm$. We need to draw a pair of tangents from a point $P$ on the outer circle to the inner circle.
Steps of construction:
$1.$ Draw two concentric circles with centre $O$ and radii $3\, cm$ and $5\, cm$.
$2.$ Take any point $P$ on the outer circle. Join $OP$.
$3.$ Bisect $OP$. Let $M'$ be the midpoint of $OP$.
$4.$ Taking $M'$ as the centre and $OM'$ as the radius,draw a dotted circle which intersects the inner circle at points $M$ and $P'$.
$5.$ Join $PM$ and $PP'$. Thus,$PM$ and $PP'$ are the required tangents.
$6.$ On measuring $PM$ and $PP'$,we find that $PM = PP' = 4\, cm$.
Actual calculation:
In right-angled $\triangle OMP$,$\angle PMO = 90^{\circ}$.
By Pythagoras theorem: $OP^2 = PM^2 + OM^2$
$PM^2 = OP^2 - OM^2$
$PM^2 = (5)^2 - (3)^2 = 25 - 9 = 16$
$PM = \sqrt{16} = 4\, cm$.
Hence,the length of both tangents is $4\, cm$.