+1766 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.
+410 
Draw a rectangle in the middle like so:
The width is r-13, while the length is r - 10, and the diagonal is r:
Therefore, use the pythagorean theorem.
(r−10)2+(r−13)2=r2
r=46±√10402=23±√260=23±2√65
We know because the distance of 13 to the wall, r > 13, therefore the only solution is 23+2√65.
+410
Draw a rectangle in the middle like so:
The width is r-13, while the length is r - 10, and the diagonal is r:
Therefore, use the pythagorean theorem.
(r−10)2+(r−13)2=r2
r=46±√10402=23±√260=23±2√65
We know because the distance of 13 to the wall, r > 13, therefore the only solution is 23+2√65.
