Calculating Radius of Arc over a Rectangle

Question

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I want to make a PCB for street light and I am facing difficulties in calculating the Arc over the top of the casting.

The Dimensions are :
L = 180 mm ( Length of the rectangle )
B = 90 mm
L from Top of the ARC = 195 mm.

How do I calculate the Arc radius that joins the rectangle.

I have included the image for better understanding.

Answer 1

If I understand correctly your question, the figure shows the solution.

If $x$ is the radius $\overline{AF}$ than $$ \overline{AG}^2+(x-\overline{EG})^2=x^2 $$

so, in your case, $x$ is the solution of the equation $$ 45^2+(x-15)^2=x^2 $$