Question

Type the correct answer in the box. Use numerals instead of words. If necessary, use / for the fraction bar.

In the given diagram, two sets of arcs are drawn above and below segment AB using a compass set to the same width. For one set of arcs, the compass needle is positioned at point A. For the second set of arcs, the compass needle is positioned at point B. A line drawn through the intersections of these two sets of arcs determines the location of point C.

Answer 1

Answer: CB: 16, AB: 32 (units)

Explanation:

The question mentioned that the compass was set to the same width, indicating that any arc drawn from the same point will have same distance from its origin.

In this case, if can represent the intersection above the segment as D and the intersection below the segment as E and extend the points in a shape as:

Triangle ADE and

Triangle BDE.

Since they share the base,

and as the distance from

A to D,

A to E,

B to D,

and B to E

are same as mentioned above("the compass was set to the same width, indicating that any arc drawn from the same point will have same distance from its origin.")

We can conclude congruence between ADE and BDE.

Congruent triangles have identical shape and therefore same heights(AC and BC).

And therefore, line BC is 16 units and line AB is 32 units.