Question

Construct tangents to a circle of radius $4cm$ at $Q$ and $R$, from a point $P$ on the concentric circle of radius $6cm$.

Answer 1

Steps of construction
1. Draw two concentric circles having radii $4cm$ and $6cm$. $O$ is the centre of the circles.
2. Take any point $P$ on the larger circle.
3. Join $OP$. Mark two arcs of equal length from $O$ and $P$ and join the intersection point of the arcs. Mark the intersection point of the perpendicular bisector as mid-point $M$ of $OP$
4. Taking $M$ as centre and radius $=MP=MO$, draw circle which intersects the smaller circle in two points $Q$ and $R$.
5. Join $PQ$ and $PR$.

Now $PQ$ and $PR$ are the required tangents. By measurement, we have length of the tangents $=4.4cm$ (approx.)
By calculation, we have length of the tangents $=\sqrt{O{P}^2-O{Q}^2}=\sqrt{36-16}=\sqrt{20}=2\sqrt{5}cm=4.47cm$