Math, asked by sakchamgupta05, 4 months ago

Find the length of tangent drawn to a circle of radius 5cm, from a point at a distance of 15cm from the center.​

Answers

Answered by princessbueno78
0

Answer:

Answer:

Length of the tangent = 12 cm

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

Stepbystepexplanation:

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}}∠BAC = 90°

•°• Δ BAC is a right angled triangle.

By Pythagoras theorem :

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

2

=(AB)

2

)+(AC)

2

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

2

=(5)

2

)+(x)

2

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

2

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

2

\rightarrow→ \bold{144= (x)^2}144=(x)

2

\rightarrow→ \bold{\sqrt{144}=x}

144

=x

\rightarrow→ \bold{12=x}12=x

•°• Length of tangent = x = 12 cm

Step-by-step explanation:

hope it's help☺

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