How the Altitude Divides the Hypotenuse

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Draw the altitude to the hypotenuse of a right triangle. Then each leg is the geometric mean of the hypotenuse and the segment of the hypotenuse adjacent to that leg: and
. Also, the length of the altitude is the geometric mean of the two segments:
.
Contributed by: Jay Warendorff (March 2011)
Open content licensed under CC BY-NC-SA
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"How the Altitude Divides the Hypotenuse"
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Published: March 7 2011