Question

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

Answer 1

$\left(1\right)$Draw two concentric circle $C_1$ and $C_2$ with common center

0 and radius $4cm$ and $6cm$

$\left(2\right)$ Take a point P on the outer circle $C_2$ and join OP.

$\left(3\right)$ Draw the bisector of OP which bisect OP at M'.

$\left(4\right)$ Taking M' as center and OM' as radius draw a dotted circle which

cut the inner circle $C_1$ at two point M and P.

$\left(5\right)$ Join PM and PP'. Thus, PM and PP' are required tangent.

On measuring PM and PP'.

$\begin{array}{c}PM=P{P}^{\prime }=4.4cm\\ Bycalculation:\\ In\Delta OMP,\angle PMO={90}^0\\ P{M}^2=O{P}^2-O{M}^2\left(bypythagorastheorem\right)\\ P{M}^2={\left(6\right)}^2-{\left(4\right)}^2\\ =36-16=20\\ P{M}^2=20cm\\ PM=\sqrt{20}=4.4cm\\ Hence,\\ thelengthofthe\tan gentis4.4cm\end{array}$