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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 6 from one wall, and a distance of 6 from the other wall.  Find the radius of the table.

 
 Oct 21, 2024

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Find the radius of the table.

 

\(2r^2=( \sqrt{2\cdot 6^2}+r)^2\\ 2r^2=(6\sqrt{2}+r)^2 \ |^\sqrt{}\\ r\sqrt{2}=6\sqrt{2}+r\\ r(\sqrt{2}-1)=6\sqrt{2}\\ r=\dfrac{6\sqrt{2}}{\sqrt{2}-1}\\ \color{blue}r=20.485\)

 

The radius of the table is 20.485

 

laugh !

 Oct 22, 2024

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