Question

In the adjoining figure O is the centre of a circle with radius 6 cm. A is any point outside the
circle and AT is a tangent of the circle. Find the length of tangent AT, if OA - 10 cm​

Answer 1

★ ${\underline{\underline{\purple{\bold{Given:-}}}}}$

• In a adjoining figure , O is the centre of a circle with radius 6 cm.
• A is any point outside the circle and AT is a tangent of the circle .
• AO = 10 cm

★ ${\underline{\underline{\purple{\bold{To\:find:-}}}}}$

• Length of the tangent AT .

★ ${\underline{\underline{\purple{\bold{Solution:-}}}}}$

In the adjoining figure,

• Radius ( OT) = 6 cm
• OA = 10 cm

AT is the tangent of the circle .

• OT _|_ AT

∆ ATO is a right triangle .

Now, apply 'Pythagoras Theorem' :-

$\implies\sf{AT^2+OT^2=AO^2}$

$\implies\sf{AT^2+(6)^2=10^2}$

$\implies\sf{AT^2+36=100}$

$\implies\sf{AT^2=100-36}$

$\implies\sf{AT^2=64}$

$\implies\sf{AT=\sqrt{64}}$

$\implies\sf{AT=8}$

Therefore, the length of the tangent AT is 8 cm.