Problem of intersecting circles

Question

We have point p1. Draw a circle c1 from p1 with radius r1.

We have point p2. Distance between p1 and p2 (d) equals r1. (p2 is on the perimeter of c1).

Draw a circle c2 from point p2 with radius r2.

r2 is greater than r1.

The intersecting area of these two circles is half of the area of c1.

Calculate r2.

What if r1 = 10?

Answer 1

when r₁=1 ,,,In a problem sketch, can see if r₂=√2 then intersecting area is greater than (area c1)/2 and for reference if r₂=1 then intersecting area is less than (area c1)/2.

so 1<r₂<√2.

After using calculus, my analysis indicates (r₂)²≈1.21,,,r₂≈1.1

let me know if you need to see analysis.

r₁=10,,,r₂≈11.