Answer: B
What we have:

Distance from (a,b) to origin (0,0) = √((a-0)^2 + (b-0)^2) = √(a^2 + b^2)
Distance from (c,d) to origin (0,0) = √((c-0)^2 + (d-0)^2) = √(c^2 + d^2)
It is said that points (a, b) and (c, d) are equidistant from the origin. It means their distances from origin are equal, so:
√(a^2 + b^2) = √(c^2 + d^2) , both sides to power2:
a^2 + b^2 = c^2 + d^2

As it is said that |a| > |c| so we can conclude that |a|^2 > |c|^2 [They are both positive, thus when they are in the same power, their comparison result will be just the same as when the power is 1.]
Now that we know a^2 > c^2 and a^2 + b^2 = c^2 + d^2, so we can construe that b^2 is less than d^2 and so |b| is less than |d| (b and d don’t necessarily have the same relation) B is bigger than A