The rectangle tucked into a quarter circle
A quarter circle has radius r. Inside it a rectangle is drawn so that one corner of the rectangle sits exactly at the centre of the circle, two sides lie along the two straight edges of the quarter circle, and the corner opposite the centre lies on the arc.
Now draw the rectangle's other diagonal, the one that does not touch the centre.
How long is it? No dimensions of the rectangle are given.
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You have not been told the rectangle's sides, so the answer cannot depend on them. What do you know about the two diagonals of any rectangle?
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