The geometric mean of two numbers a and b is sqrt(ab). Construct the geometric mean using compass and straight edge method?

1 Answer
P dilip_k
Sep 17, 2016

DRAWNDRAWN

The lengths of two line segments are a and b. We are to determine the geometric mean of a and b using compass and straight edge method

Steps followed

  • "Two line segments of given lengths a and b are drawn by srtaight edge"

  • "A line segment OX> a+b is drawn similarly"

  • "OA = a and AB = b are taken from OX with the help of a compass"

  • "OB is bisected at Y with the help of Ruler and Compass"

  • "A semicircle of diameter OB is drawn centering Y with the help of a Compass"

  • "AP is the perpendicular drawn on OB with the help of a compass and Ruler"

  • "AP intersects the semicircle at P"
  • "The length of AP is the geometric mean of a and b"
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