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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 $10$ from one wall, and a distance of $13$ from the other wall.  Find the radius of the table.

 Jun 21, 2024

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 #1
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Pythagorean Theorem

 

(r - 10)^2  + ( r -13)^2  = r^2      simplify

 

2r^2 - 46r + 269  = r^2

 

r^2 - 46r + 269  = 0

 

r^2 -46r  + 529  = -269 + 529

 

(r - 23)^2  = 260      take the positive root

 

r - 23 = sqrt 260

 

r - 23  =   2sqrt 65

 

r = 2sqrt 65 + 23 ≈ 39.125

 

cool cool cool

 Jun 21, 2024

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