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MathNet 2013 Question 41

Math Olympiad Vault · MathNet 2013

Question 41

Slide a square of side $10$ cm in the plane $OXY$ so that the endpoints of one side always touch the coordinate axes, one on $OX$ and the other on $OY$. Determine the loci traced by:

$1.$ The midpoint of the side touching the axes.

$2.$ The centre of the square.

$3.$ The vertices of the touching side and of the opposite side in the first quadrant.