Chapter 1.3, Problem 71HP

To determine

To Find: The explanation for construction for the segment drawn $AB$ by the compass and straightedge by constructing the segment $\overline{CD}$ such that $CD=5\frac{1}{4}AB$ .

Answer to Problem 71HP

The explanation for the construction and the construction is obtained.

Explanation of Solution

Consider the line segment as shown in Figure 1

  

Figure 1

Consider the point m and select the point C on m then draw the arc centred at C with the radius AB such that the arc intersect m at the point $P_1$ and repeat the process such that $C{P}_6=6\left(AB\right)$ .

The next step is to draw the perpendicular bisector of $\overline{P_5{P}_6}$ twice and then denote $Q_1$ and D to the two point of the intersection $CD=5\frac{1}{4}AB$ as shown in Figure 2.

  

Figure 2