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Problem 590

Construct the segment of length equal to \(\mathrm{a} \cdot \mathrm{b}\) where a and \(\mathrm{b}\) are the lengths of the segments below. (Unit length is shown below.)

Expert verified

Draw a line segment AB with lengths AC = a and BC = b. Draw circles centered at A and B with radius (a + b). Let the circles intersect at points D and E. Draw line segments DE and AD. Draw a line parallel to DE through B, intersecting circle A at F. The length of segment AF represents \(a \cdot b\), due to similarity of triangles ADE and ABF.

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Chapter 30

Construct an angle containing \(60^{\circ}\), whose vertex is a given point. (See figure).

Chapter 30

Construct the perpendicular bisector of a given segment. Bisect a given angle.

Chapter 30

Divide any segment into three congruent segments.

Chapter 30

Construct a line perpendicular to a given line through a given point outside the line.

Chapter 30

Construct the mean proportional between two given segments.

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