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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 22, 2024

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(r -6)^2  +(r -6)^2  =r^2

 

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

 

2[ r^2 -12r + 36 ]= 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 = 12 + sqrt (72)  =  12 + 6sqrt 2  =  6 ( 2 + sqrt 2)

 

cool cool cool

 Jun 22, 2024

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