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Open systems with balanced gain and loss, described by parity-time reversal (PT) symmetric Hamiltonians have been deeply explored over the past decade. Most explorations are limited to finite discrete models (in real or reciprocal spaces) or continuum problems in one dimension. As a result, these models do not leverage the complexity and variability of two-dimensional continuum problems on a compact support. Here, we investigate eigenvalues of the Schrödinger equation on a disk with zero boundary condition, in the presence of constant, PT-symmetric, gain-loss potential that is confined to two mirror-symmetric disks. We find a rich variety of exceptional points, re-entrant PT-symmetric phases, and a nonmonotonic dependence of the PT-symmetry breaking threshold on the system parameters. By comparing results of two model variations, we show that this simple model of a multicore fiber supports propagating modes in the presence of gain and loss.