Me Want a Heart Limb!

Mai Valentine planned to prepare a cake for Valentine's Day. While sketching out shapes and polygons, she thought about creating a heart shape, which resembles a combination of 3 semicircles of radii r1r_1, r2r_2 and r1+r2r_1 + r_2, where r1r2r_1 \leq r_2. Joey Wheeler wants to take a limb as indicated by the dashed line. He claims that

After removing a limb, the new shape's area is half the original area of the heart.

What is the ratio of r2r_2 to r1r_1 that satisfies the given statement?

This is the end of the first chapter of the story. Check the following chapter directory if you are interested:

First - Second - Third - Fourth - Fifth


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