A circular table is pushed into a corner of a rectangular room so that it touches both walls. A point on the edge of the table between the two points of contact is 2 cm from one wall and 9 cm from the other wall. Find the radius of the table.

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anonymous · Answer

sorry for the horrible paint drawing of the table, but here we go. where the table touches the walls will create a 90 degree angle with the center of the table. using the knowledge that a 45-45-90 triangle's hypotenuse is $$h=x \sqrt{2}$$ the length between the two point on the wall is $$r \sqrt{2}$$ with r being the radius. that makes one side of a triangle, the other two points come from the points of the table hitting the walls and the point on the table. looking at my poor picture you can (hopefully) see that you make a triangle with side 9cm, 2cm, and  $$r \sqrt{2}$$ cm. after that i dont actually know what to do, i would think using triginometry somehow, sorry i couldnt finish, but i have to go. i hope i helped

anonymous · Answer

thanks