see the figure..

angle QPR = angle SRP = angle PXR = 90⁰

now,  consider triangle PQR , PQ = 2r tanb  ---------------(1)

//ly, RS = 2r tana --------------------(2)

now, from triangle PXR, a + b =90⁰ -----------(3)

from (2) and (3)

RS = 2r cotb --------------------(4)

multiplying (1) and (4)

we get, PQ.RS = (2r)²

so, 2r = (PQ.RS)^1/2, hence option A is correct :)