Tidally locked planet in binary star system?

Essentially, two stars of identical mass but different temperatures are in a binary system. One planet is directly in their barycenter, tidally locked to one and therefore both stars. The effect I'm going for is one half of the planet is daylight by a bright white/blue star, and the other is "night" even though it's lit by the other star which is red.

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Tidally locked planet in binary star system?

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