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
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"#
