Question

In the given figure, if AT is a tangent to the circles with centre O, such that OT=4cm

and ‹OTA=300, then find the length of AT (in cm)​

Answer 1

$\sf{\bold{\blue{\underline{\underline{Given}}}}}$

AT is tangent to the circle with centre "O".

☆ OT=4cm.

☆$\tt{\angle{OTA}=30°}$⠀⠀

$\sf{\bold{\red{\underline{\underline{To\:Find}}}}}$

¤ $\tt{Value~ of ~AT}$? ¤⠀⠀

$\sf{\bold{\purple{\underline{\underline{Solution}}}}}$

Here,

in $\triangle{OAT}$,$OA ⊥ AT$

So,

$\angle{OTA}=90°$

$\therefore$ $\triangle{OAT}$ is a right angle triangle.

And, $\tt{\angle{OTA}=30°}$,OT=4cm.

Thus,

$\boxed{\orange{Cos\theta=\dfrac{Base}{Hypothesize}}}$

$\rightsquigarrow$ :$\tt{cos\angle{OTA}=\dfrac{AT}{OT}}$

$\rightsquigarrow$ :$\tt{cos30°=\dfrac{AT}{OT}}$

$\rightsquigarrow$ :$\tt{\dfrac{\sqrt{3}}{2}=\dfrac{AT}{OT}}$

$\rightsquigarrow$ :$\tt{\dfrac{\sqrt{3}}{2}=\dfrac{AT}{4}}$($\because{AT=4}$)

$\rightsquigarrow$ :$\tt{AT=\dfrac{\sqrt{3}}{2}×4 }$

$\rightsquigarrow$ :$\tt{AT=\dfrac{\sqrt{3}}{\cancel{2}}×\cancel{4}}$

$\rightsquigarrow$ :$\tt{AT=2\sqrt{3}}$

⠀⠀

⠀⠀⠀⠀

$\sf{\bold{\green{\underline{\underline{Answer}}}}}$

⠀⠀⠀⠀

$\therefore$ Value of $\pink{\underline{AT=2\sqrt{3}}}$

Answer 2

Step-by-step explanation:

refre the photo for answer