The geometric mean of two numbers a and b is sqrt(ab). Construct the geometric mean using compass and straight edge method?
1 Answer
Sep 17, 2016
DRAWN
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
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"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"