Question

Construct a tangent to a circle of radius $4cm$ from a point on the concentric circle of radius $6cm$ and measure its length. Also verify the measurement by actual calculation.

Answer 1

In order to do the desired construction, we follow the following steps:

$StepsI$: Take a point $O$ on the plane of the paper and draw a circle of radius $OA=4cm$. also draw concentric circle of radius $OB=6cm.$

$StepsII$: Find the mid-point $C$ of $OB$ and draw a circle of radius $OC=BC$. Suppose this circle intersect the circle of radius $4cm$ at $P$ and $Q$

$StepsIII$: Join $BP$ and $BQ$ to get the desired tangents from a point $B$ on the circle of radius $6cm.$
By actual measurement, we find the $BP=BQ=4.5cm$

$Justification:$

In $△BPO$, we have
$OB=6cm$ and $OP=4cm$
$\therefore {OB}^2={BP}^2+{OP}^2$ [using pythagoras theore]
$\Rightarrow BP=\sqrt{{OB}^2-{OP}^2}$
$\Rightarrow BP=\sqrt{36-16}=\sqrt{20}cm=4.47cm=5cm$
Similarly, $BQ=4.47cm$ $\simeq 4.5cm$