Chapter 6.4, Problem 12WE

To determine

To find: the longest segment.

Answer to Problem 12WE

  $\overline{CD}$ is the longest side.

Explanation of Solution

Given Information:

Given diagram,

  

Calculation:

Consider the theorem,

If one angle of a triangle is larger than a second angle, then the side opposite the first angle is longer than the side opposite the second angle.

First draw the diagram to scale as below:

  

From the above figure it can be observed that all $\angle B,\angle C$ and $\angle D$ are right angles so $OA,OB,OC$ will be the largest sides will have equal lengths because they all are radii of the circular arc which has $O$ as center.

Therefore, according to the above theorem, $CD$ will be the longest side.

Hence, $\overline{CD}$ is the longest side.