Rotating a Triangle

Geometry Level 5

Acute triangle ABCABC has its vertices labeled in a clockwise manner. It is rotated 9090^\circ counter-clockwise about CC to get ABCA’B’C. Let DD be the midpoint of ABAB’. If BA=1202 \lvert BA’ \rvert = 1202 , what is CD \lvert CD \rvert ?

Details and assumptions

XY|XY| denotes the straight line distance from XX to YY.
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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