+1725 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 $1$ from one wall, and a distance of $1$ from the other wall. Find the radius of the table.
+36943 See image
Using ratios,
'1' is to 'r' as sqrt(2) is to sqrt(2) + r ......or:
1/r = sqrt(2) / (r + sqrt(2) ) <======solve for 'r' ..... cross multiply
r + sqrt 2 = r sqrt 2
r - r sqrt 2 = - sqrt 2
r ( 1 - sqrt 2) = - sqrt2
r = sqrt (2) / ( sqrt2 -1)
r = 2 + sqrt 2 = 3.414 units
+36943 See image
Using ratios,
'1' is to 'r' as sqrt(2) is to sqrt(2) + r ......or:
1/r = sqrt(2) / (r + sqrt(2) ) <======solve for 'r' ..... cross multiply
r + sqrt 2 = r sqrt 2
r - r sqrt 2 = - sqrt 2
r ( 1 - sqrt 2) = - sqrt2
r = sqrt (2) / ( sqrt2 -1)
r = 2 + sqrt 2 = 3.414 units
