Question

This is a cross-sectional view of candy bar ABC. A candy company wants to create a cylindrical container for candy bar ABC so that it is circumscribed about the candy bar. If segment AD = 4 cm, what is the smallest diameter of wrapper that will fit the candy bar? Triangle ABC in which point E is between points A and B, point D is between points A and C, point F is between points B and C, segments AE and EB are congruent, segments BF and FC are congruent, and angles AED, ABF, and DFC are right angles.

Answer 1

8 cm

Explanation:

When a right triangle is circumscribed in a circle, the diameter is the hypotenuse AC.

Therefore, the smallest diameter of the wrapper will be that of the circle whose diameter has endpoints of A and C.

From the diagram:

• AE=DF
• ED=FC

Therefore, Triangle AED is congruent to Triangle DFC and in fact AD=DC.

Given: AD =4 cm

Therefore, the smallest diameter

AC=AD+DC

=4+4

=8 cm