Geometry

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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.

AnswerscorrectIy Oct 21, 2024

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asinus · Answer 1 · 2024-10-22T06:56:42

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

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