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The centre of the (secondary of the) centre tapped transformer is zero volts because that is the point in the circuit on which you based your measurement. If you were to connect the reference meter lead to the end of the winding, then the centre tap would have voltage on it. Its all a matter of perspective, i.e. reference.

It also happens that the centre tap is usually grounded and, since you usually connect the meter's reference lead to ground, if you connect the meter's reading lead to the same point, you would logically expect there to be a zero volts differential. Its the same as connecting the two leads together.

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