Question

the lenght of a tangent from a point A at a distance 70 cm from the centre of a circle is 56 cm .find the circumference of the circle. ​

Answer 1

● See the attachment diagram.

$\begin{lgathered}\Large\sf\pink{Given} \\\end{lgathered}$

$\sf{\red{Length\:of\:tangent}}\:(AP)\:=\:56\:cm\:$

$\sf{\red{Length\:of\:pt.\:\atop {of\:the\:circle}}\:(OA)\:=\:70\:cm}\:$

(OA)=70cm

$\begin{lgathered}\Large\sf\purple{Formula,} \\\end{lgathered}$

▪ To calculate radius of the circle,

$\begin{lgathered}\green\bigstar\:\:\sf\blue{Radius\:(OP)\:=\:\sqrt{(OA)^2\:-\:(AP)^2}\:} \\\end{lgathered}$

$\begin{lgathered}\Large\sf\orange{Calculation,} \\\end{lgathered}$

$\begin{lgathered}:\implies\:\:\sf{Radius\:(OP)\:=\:\sqrt{(70)^2\:-\:(56)^2}\:} \\\end{lgathered}$

$\begin{lgathered}:\implies\:\:\bf{Radius\:(OP)\:=\:\sqrt{4900\:-\:3136}\:} \\\end{lgathered}$

$\begin{lgathered}:\implies\:\:\sf{Radius\:(OP)\:=\:\sqrt{1764}\:} \\\end{lgathered}$

$\begin{lgathered}:\implies\:\:\sf\green{Radius\:(OP)\:=\:42\:cm\:} \\\end{lgathered}$

▪ To calculate circumference of the circle,

$\begin{lgathered}\red\bigstar\:\:\sf\orange{Circumference \:=\:2\pi {r}\:} \\\end{lgathered}$

$\begin{lgathered}\longmapsto\:\:\sf{Circumference \:=\:2\times {\dfrac{22}{7}}\times {42}\:} \\\end{lgathered}$

$\begin{lgathered}\longmapsto\:\:\sf{Circumference \:=\:2\times{22}\times {6}\:} \\\end{lgathered}$