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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.

 Jan 20, 2025

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avatar+130315 
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(r-6)^2 + (r-6)^2  = r^2

 

2r^2 - 24r + 72  =  r^2

 

r^2 - 24r + 72 = 0     complete the square on r 

r^2 -24r + 144 = -72 + 144

 

(r -12)^2 = 72

 

r - 12  = sqrt [72]

 

r = 12 + 6sqrt 2

 

cool cool cool

 Jan 20, 2025

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