### Brain Teasers

# Segment Redirected

The professor drew a circle in the blackboard. He marked the center and named it A.

Then he made a horizontal segment starting at the center and ending on the circle at point B. He named it Segment AB.

Then he made a vertical segment, perpendicular to AB, starting at A and ending on the circle at point C. He named it Segment AC.

Then he marked a point somewhere in the middle of AC and named it X. He started at X and made another horizontal segment, parallel to AB and perpendicular to AC, and ended it on the circle at point Y. He named it segment XY.

Then He started at point Y at the circumference, and made another segment, parallel to AC and perpendicular to AB, that ended in a point around the middle of AB at a point that he called W.

Then we saw the blackboard and there was a circle with a perfect rectangle in it, the rectangle made of points AXYW.

The professor then drew the last segment, from point X to point W, making then the diagonal segment XW of the rectangle.

And He asked: If the diameter of the circle is 1 inch, then how long is the segment XW?

Then he made a horizontal segment starting at the center and ending on the circle at point B. He named it Segment AB.

Then he made a vertical segment, perpendicular to AB, starting at A and ending on the circle at point C. He named it Segment AC.

Then he marked a point somewhere in the middle of AC and named it X. He started at X and made another horizontal segment, parallel to AB and perpendicular to AC, and ended it on the circle at point Y. He named it segment XY.

Then He started at point Y at the circumference, and made another segment, parallel to AC and perpendicular to AB, that ended in a point around the middle of AB at a point that he called W.

Then we saw the blackboard and there was a circle with a perfect rectangle in it, the rectangle made of points AXYW.

The professor then drew the last segment, from point X to point W, making then the diagonal segment XW of the rectangle.

And He asked: If the diameter of the circle is 1 inch, then how long is the segment XW?

### Answer

XW is 1/2 inch long, because both diagonals of a rectangle are equal, and the other diagonal (AY) makes up the radius of the circle, that is half the diameter.Hide Answer Show Answer

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