Since they're all part of the same shape, the different lines and segments in a circle are related in ways that can help you solve problems if you're given some information about the circle. As you work through these problems, try to identify the relationship between the radius and the diameter of a circle.
Problem 1
Problem 2
In this circle, AC = 5. Find the measure of AB.
\(\small\mathsf{ \overline {AC}}\) is a radius, and \(\small\mathsf{ \overline {AB}}\) is a diameter, a chord that goes through the center of the circle.
If you know that AC = 5 and you can see that AC represents one half of the diameter, then you can calculate that AB = 10.
In the following circle AB = 9. Find the measure of AC.
Segment AB is a diameter. Since AB = 9, then AC = 4.5.
Question
Based on these two problems, what is the relationship between the radius and diameter of a circle?
In mathematical terms, \(\mathsf{ r = \frac{d}{2} }\)
