Question

Find the length of the tangent from a point M which is at a distance of 17 cm from the centre O of the circle of radius 8 cm.​

Answer 1

$\huge\star\underline {\mathtt \orange{❥A} \mathfrak\blue{n}\mathfrak\blue{s} \mathbb\purple{ w}\mathtt\orange{e} \mathbb\pink{r}}\star\:$

Let O is the center of the circle and tangent touches the circle at point T.

Then, triangle OPT will be a right angle triangle.

We are given,

OP=17cm,OT=radius = 8cm

So, PT2=OP2−OT2

PT2=172−82=289−64=225

PT=225−−−√=15cm

So, length of tangent will be 15 cm

Answer 2

Answer:

$\huge \underbrace \pink{★ Answer❀✿°᭄★}$

$length \: of \: tangent( \: l \: ) = 15cm$

$Given \: distance ( \: d \: ) = 17cm \\ radius \: of \: the \: circle( \: r \: ) = 8cm \\let \: length \: of \: the \: tangent = l \: cm$

$⇒ \: \sqrt{d ^{2} - {r}^{2} } \\ ⇒ \: \sqrt{17 ^{2} - {8}^{2} } \\ ⇒ \: \sqrt{(17 + 8)(17 - 8)} \\ ⇒ \: \sqrt{25 \times 9} \\ ⇒ \: 5 \times 3 \\ ⇒ \: 15cm$

$length \: of \: tangent \: ( \: l \: ) = 15cm.$

$\huge \pink{hope \: it \: helps \: u}$