The phase diagram of the superconducting high-Tc cuprates is governed by two energy scales: T*, the temperature below which a gap is opened in the excitation spectrum, and Tc, the superconducting transition temperature. The way these two energy scales are reflected in the low-temperature energy gap is being intensively debated. Using Zn substitution and carefully controlled annealing we prepared a set of samples having the same T* but different Tc's, and measured their gap using Angle Resolved Photoemission Spectroscopy (ARPES). We show that Tc is not related to the gap shape or size, but it controls the size of the coherence peak at the gap edge.