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Two parallel chords in a circle of radius 7.5cm measure 12cm and 9cm. They are on the same side of the circle. What is the distance between them?

Guest Jul 3, 2015

Best Answer 

 #1
avatar+88830 
+10

Here's one method.....but.....maybe not the fastest one !!!

 

Let the center of the circle lie at the origin and let both chords be parallel to the x axis.

 

The equation of the circle  is  x^2 + y^2   = 56.25

 

The chord of 12 cm in  length will have one of its endpoints at  (6,y1)......and y1 =

 

√[56.25 - 6^2] = √[56.25 -36 ]  = 4.5  { taking the positive value of the  root  }

 

And

The chord of 9 cm in  length will have one of its endpoints at  (4.5, y2)......and y2 =

 

√[56.25 - 4.5^2] = √[56.25 - 20.25 ]  = 6   {again, taking the positive value of the root}

 

So....the distance between the chords is  y2 - y1  = 6 - 4.5   = 1.5 cm

 

Here's a pic.....

 

 

Note that ED = 9, CB = 12 and  FG = 1.5

 

 

CPhill  Jul 3, 2015
 #1
avatar+88830 
+10
Best Answer

Here's one method.....but.....maybe not the fastest one !!!

 

Let the center of the circle lie at the origin and let both chords be parallel to the x axis.

 

The equation of the circle  is  x^2 + y^2   = 56.25

 

The chord of 12 cm in  length will have one of its endpoints at  (6,y1)......and y1 =

 

√[56.25 - 6^2] = √[56.25 -36 ]  = 4.5  { taking the positive value of the  root  }

 

And

The chord of 9 cm in  length will have one of its endpoints at  (4.5, y2)......and y2 =

 

√[56.25 - 4.5^2] = √[56.25 - 20.25 ]  = 6   {again, taking the positive value of the root}

 

So....the distance between the chords is  y2 - y1  = 6 - 4.5   = 1.5 cm

 

Here's a pic.....

 

 

Note that ED = 9, CB = 12 and  FG = 1.5

 

 

CPhill  Jul 3, 2015

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