Question

3. Find the length of a tangent drawn to a circle, with radius 5 cm, from a point 13 cm
away from the centre of the circle.
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Answer 1

Answer:

it is your answer like my answer

Answer 2

$\bold{\underline{\underline{Answer:}}}$

Length of the tangent = 12 cm

$\bold{\underline{\underline{Step\:by\:step\:explanation:}}}$

Given :

• Radius = 5 cm
• Tangent drawn from a point 13 cm away from the centre of the circle.

To find :

• Length of the tangent

Solution :

We have the radius = 5 cm and the distance from the centre of the circle to the point from where the tangent is drawn = 13 cm.

Let AB = radius = 5 cm

Let BC = point from the centre from where the tangent is drawn = 13 cm

From tangent theorem :-

• A tangent at any point of a circle is perpendicular to the radius at the point of contact.

•°• In Δ ABC, m $\bold{\angle{BAC}}$ = 90°

•°• Δ BAC is a right angled triangle.

By Pythagoras theorem :

$\bold{(Hypotenuse)^2\:=\:(Side1^2)+(Side2)^2}$

Hypotenuse = BC = 13 cm

Side 1 = AB = 5 cm

Side 2 = AC = x cm

Block in the values,

$\rightarrow$$\bold{(BC)^2\:=\:(AB)^2)+(AC)^2}$

$\rightarrow$$\bold{(13)^2\:=\:(5)^2)+(x)^2}$

$\rightarrow$$\bold{169\:=\:25+(x)^2}$

$\rightarrow$$\bold{169-25= (x)^2}$

$\rightarrow$$\bold{144= (x)^2}$

$\rightarrow$$\bold{\sqrt{144}=x}$

$\rightarrow$$\bold{12=x}$

•°• Length of tangent = x = 12 cm