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