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# Geometry

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A circle is placed in a 90 degree corner, and that circle is touching both walls of that corner. a point on the circumference of the circle is 18 inches from one wall and 35 inches from the other wall. what is the radius of the circle? if some work could be shown it would be very nice to know for the future.

Jun 15, 2021

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No that's absolutely wrong! Idk who you're but pls stop giving wrong answers on every question you find. You're not obliged to answer, if you don't know just leave it.

amygdaleon305  Jun 15, 2021
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Let's assume the corner of the wall is at (0,0) and P be the point, then the centre of circle is at (r,r). Then equation of  circle is

\((x-r)^2+(y-r)^2= r^2\)

And, according to question, points (18,35) and/or (35,18) lies on the circle.

Take any of them it doesn't make any difference

⇒ \((18-r)^2+(35-r)^2=r^2\)

⇒ \(324-36r+r^2+1225-70r+r^2=r^2\)

⇒ \(r^2-106r+1549=0\)

Solving this we get

\(r=88.5 \)  and  \(r=17.5\)

Hence, the radius can be either 88.5 inches or 17.5 inches.

Jun 15, 2021