i got the right answer that is a but can some walk me through choosing numbers approach or algebra

i just eye balled it. I was thinking about something like Ar. of O + Ar. of P - 2 Ar. of O to P but could not figure it out

that was my initial thought but i was trying to figure out that “Something”

You can simply show that the shaded region is greater than half the circle’s area (for instance, by taking the tangent at point O).

It is still possible to use algebra if you want, but that’s relatively complex in comparison.