+1855 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.
+1950 Let's first graph this problem to have a visual on what we must do.
First off, let's note we have a lot of right triangles to work with. This also means we almost certainly must use the pythaogrean thereom.
So let's do it. First, we have the equation
(r−6)2+(r−6)2=r22r2−24r+72=r2r2−24r+72=0
Now, let's complete the square for r.
r2−24r=−72r2−24r+144=−72+144(r−12)2=72
since the distance cannot be negative, let's take the positive root for r. We have
r−12=√72r=√72+12r=6√2+12≈20.49
So 20.49 is our answer.
Thanks! :)
