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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 6 from one wall, and a distance of 6 from the other wall.  Find the radius of the table.

 Jun 2, 2024

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 #1
avatar+129895 
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Pythagorean Theorem

 

(r -6)^2 + (r - 6)^2 = r^2

 

2r^2 - 24r + 72  = r^2

 

r^2 - 24r + 72 =  0

 

r^2 - 24r   =  -72

 

r^2 -24r + 144  = -72 + 144

 

(r- 12)^2  = 72       take the positive root

 

r -12   =  sqrt (72)

 

r =   sqrt (72) + 12

 

r = 6sqrt (2) + 12  ≈  20.49

 

 

 

 

cool cool cool

 Jun 2, 2024

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