Consider below circles drawn on A4 sheet of paper. The red circles have diameter equal to half of the A4 paper height and the pink-green circles have diameter equals to width and height respectively. Find the coordinates of intersecting point P, considering bottom-left corner point as the origin. Note: A4 size paper have a width of 210 mm and 297 mm of height.
Answers
Answer:
Consider the above picture, where you would want to find a value for r, depending on R so that the conjoint area (marked gray) is equal to half the area of the orange circle, i.e.
A(r)=12πR2
Come up with a way to find r, if the blue circle's centre is located on the perimeter of the orange circle.
I'm okay with using Mathematica if necessary, I just can't seem to find a way to solve my problem. Also allow me to streamline the wording of the problem.
Problem worded differently
If you have a circle with radius R, and you attach another circle, with its centre, on the perimeter of the first circle. Find the radius r (see first image) for the second circle such that the area between the circles is 50% of the area of the first circle.
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