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Suppose that the area between a pair of concentric circles is 49pi. Find the length of a chord in the larger circle that is tangent to the smaller circle.

Respuesta :

lublana

Answer:

14 units

Step-by-step explanation:

We are given that the area between two concentric circles is [tex]49\pi[/tex]

We have to find the length of chord in the larger circle that is tangent to the smaller circle.

Let [tex]r_1,r_2[/tex] be the radius of two circles.

[tex]r_1[/tex] be the radius of small circle and [tex]r_2[/tex] be the radius of large circle

We know that area pf circle=[tex]\pi r^2[/tex]

Area of large circle =[tex]\pi r^2_2[/tex]

Area of small circle =[tex]\pi r^2_1[/tex]

Area between two circles =[tex]49\pi[/tex]

Area of large circle -Area of small circle=[tex]49\pi[/tex]

[tex]\pi r^2_2-\pi r^2_1=49\pi[/tex]

[tex]\pi(r^2_2-r^2_1)=49[/tex]

By pythagorus theorem

[tex]AD^2=OA^2-OD^2[/tex]

[tex]AD^2=r^2_2-r^2_1[/tex]

[tex]AD=49[/tex]

[tex]AD=\sqrt{49}=7[/tex]

Length of chord=[tex]2\cdot AD[/tex]

Hence, the length of chord of the larger circle =[tex]2\cdot7=14[/tex] units

Ver imagen lublana

Answer :

Length of chord is 14 units long in the larger circle that is tangent to the smaller circle.

Explanation :

Given that,

Area between a pair of concentric circles = 49π  

We need to find the length of a chord in the larger circle that is tangent to the smaller circle.

Let R be the radius of larger circle.

Let r be the radius of smaller circle.

Let the length of chord be 2c

Area of space between concentric circle [tex]=\pi(R^2-r^2)[/tex]

Further Explanation:

According to question, it becomes,

[tex]\pi(R^2-r^2)=49\pi[/tex]

Therefore, [tex]R^2-r^2=49[/tex]

In ΔOAB, ∠OAB = 90° (Please find attach figure)

Using the pythagorous theorem, we get that  

[tex]c=\sqrt{R^2-r^2}[/tex]

[tex]c=\sqrt{49}[/tex]               [tex]\because R^2-r^2=49[/tex]

[tex]c=7[/tex]

Length of chord = 2c

Length of chord = 2(7)

                          = 14 units

Learn more:

https://brainly.com/question/13034352  (Answered by wagonbelleville)

Keywords :

Length of chords, Pythagorous theorem, Concentric circles

Ver imagen ridamkhare24

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