= Solution
<Limb darkening> makes the central stellar surface brighter than the disk mean. A small planet at projected position $\mathbf x$ blocks fractional <flux> approximately $\delta(\mathbf x)=(R_p/R_\star)^2I(\mathbf x)/\langle I\rangle$. A central transit is therefore deepest near mid-transit and rounded rather than flat-bottomed; a near-limb chord can be shallower. The geometrical contact times do not change for fixed radii and <orbit>, although a threshold-based measured duration can change because ingress and egress are fainter.
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