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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 5 from one wall, and a distance of 5 from the other wall. Find the radius of the table.

 Apr 30, 2024

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 #1
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(r-5)^2  + (r- 5)^2  = r^2

 

2 [ r^2 - 10r + 25 ]  =  r^2

 

2r^2 - 20r + 50  = r^2

 

r^2 - 20r  =   - 50      complete the square on r

 

r^2 - 20r + 100  =  -50 +100

 

(r - 10^2  =  50          take the positive root

 

r  - 10 = sqrt 50

 

r -10  =  5sqrt 2

 

r =  5sqrt 2 + 10  ≈  17.07

 

cool cool cool

 Apr 30, 2024

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