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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