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avatar+464 

this Question is based on cirlces

 

 
shreyas1  Oct 12, 2018

Best Answer 

 #1
avatar+7324 
+2

Let the radius of the smaller circle  =  s

Let the radius of the bigger circle  =  b

 

And let's label the point of tangency " P ".

 

 

Side  s  is drawn from the center of the circle to  P ,  so side  s  meets  AB  at a right angle.

And by the hypotenuse-leg theorem, the two triangles are congruent.  And  AB =  80  So...

 

AP + PB  =  80

                               And we know  AP  =  PB

PB + PB  =  80

 

2 * PB  =  80

 

PB  =  40

 

By the Pythagorean theorem....

 

402  +  s2  =  b2

 

1600 + s2  =  b2

 

1600  =  b2 - s2

 

area of shaded region  =  area of bigger circle - area of smaller circle

 

area of shaded region  =   π b2   -   π s2

 

area of shaded region  =  π( b2 - s2 )

 

area of shaded region  =  1600π     (sq units)   smiley

 
hectictar  Oct 12, 2018
 #1
avatar+7324 
+2
Best Answer

Let the radius of the smaller circle  =  s

Let the radius of the bigger circle  =  b

 

And let's label the point of tangency " P ".

 

 

Side  s  is drawn from the center of the circle to  P ,  so side  s  meets  AB  at a right angle.

And by the hypotenuse-leg theorem, the two triangles are congruent.  And  AB =  80  So...

 

AP + PB  =  80

                               And we know  AP  =  PB

PB + PB  =  80

 

2 * PB  =  80

 

PB  =  40

 

By the Pythagorean theorem....

 

402  +  s2  =  b2

 

1600 + s2  =  b2

 

1600  =  b2 - s2

 

area of shaded region  =  area of bigger circle - area of smaller circle

 

area of shaded region  =   π b2   -   π s2

 

area of shaded region  =  π( b2 - s2 )

 

area of shaded region  =  1600π     (sq units)   smiley

 
hectictar  Oct 12, 2018
 #2
avatar+89998 
+2

Very nice, hectictar.....!!!

 

 

cool cool cool

 
CPhill  Oct 12, 2018
 #3
avatar+464 
+1

Thank you Hectictar

 
shreyas1  Oct 13, 2018

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