Chapter 13.3, Problem 48SPR

To determine

To explain:

The type of figure $\Delta AOC$ is.

Answer to Problem 48SPR

  $\Delta AOC$ is a right isosceles triangle.

Explanation of Solution

Given information:

  

Calculation:

A stained glass that contains the points A, B, C, D, E, F, G, and H has the following design:

  

Since there are $8$ small arcs around the circle, which are given by:

  $\measuredangle AB,\measuredangle BC,\measuredangle CD,\measuredangle DE,\measuredangle EF,\measuredangle FG,\measuredangle GH,\measuredangle HA$ , and these 8 arcs are congruent, the measure of each arc is found by dividing $360°$ degrees by $8$ , which is $45°$ .

Because $\angle AOC$ is a central angle that consists of two $45°$ arcs, $\angle AOC$ is a right angle (equal to $90°$ ).

Therefore, $\Delta AOC$ is a right isosceles triangle.