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A circular table is pushed into a corner of the room, where two walls meet at a right angle.  A point $P$ on the edge of the table (as shown below) has a distance of $1$ from one wall, and a distance of $1$ from the other wall.  Find the radius of the table.

 Jan 8, 2024

Best Answer 

 #1
avatar+36919 
+1

See image 

Using ratios, 

'1' is to 'r'   as  sqrt(2) is to sqrt(2) + r ......or:

     1/r  = sqrt(2) / (r + sqrt(2) )     <======solve for 'r'   ..... cross multiply

    r + sqrt 2  = r sqrt 2 

    r - r sqrt 2 = - sqrt 2

     r ( 1 - sqrt 2)  = - sqrt2

     r =   sqrt (2) / ( sqrt2 -1) 

     r = 2 + sqrt 2     = 3.414 units 

 Jan 8, 2024
 #1
avatar+36919 
+1
Best Answer

See image 

Using ratios, 

'1' is to 'r'   as  sqrt(2) is to sqrt(2) + r ......or:

     1/r  = sqrt(2) / (r + sqrt(2) )     <======solve for 'r'   ..... cross multiply

    r + sqrt 2  = r sqrt 2 

    r - r sqrt 2 = - sqrt 2

     r ( 1 - sqrt 2)  = - sqrt2

     r =   sqrt (2) / ( sqrt2 -1) 

     r = 2 + sqrt 2     = 3.414 units 

ElectricPavlov Jan 8, 2024

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