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I want to find if the 10.3x9.8 rectangle would fit in the light green part of the circle. What equations would be used?

(There is a circuit board I need to sit level in a tube.)

Does a coordinate plane need to be used? I tried looking into this. I also tried searching for an visual online tool to merely fit a shape (rectangle) within another shape (circle).

adamaero
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The $10.3$ side of the rectangle (vertical blue line) is drawn to fit so the ends are on the circle. For the rectangle to fit in the green area the width must be less than $x+y$.

The radius of the circle is $10.5$ so $y=0.5$

The length $x$ is given by Pythagoras, so $$x=\sqrt{10.5^2-5.15^2}=\sqrt{83.7275}$$

Then $x+y=9.65027322…<9.8$ so the rectangle won’t fit.

David Quinn
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