Rotating a Triangle

Geometry Level 5

Acute triangle $$ABC$$ has its vertices labeled in a clockwise manner. It is rotated $$90^\circ$$ counter-clockwise about $$C$$ to get $$A’B’C$$. Let $$D$$ be the midpoint of $$AB’$$. If $$\lvert BA’ \rvert = 1202$$, what is $$\lvert CD \rvert$$?

Details and assumptions

$$|XY|$$ denotes the straight line distance from $$X$$ to $$Y$$.
Due to the rotation in the question, I am explicitly denoting that we are measuring the straight line distances, as opposed to the arc length of the sector.

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