Given Circle D, if AC = 16 units, then what is the length of CB?
A circle is drawn with center D. Two radii are drawn, AD and DC. Segment AC is drawn with a perpendicular, DB.
In a circle, the perpendicular from the centre to any chord bisects the chord.
Refer to your diagram to figure out the answer to the question.
To find the length of CB, we need to use the properties of a circle and the given information. Let's break down the problem step by step:
1. First, let's draw a diagram to visualize the situation. We have a circle with center D. Two radii, AD and DC, are drawn, creating a right triangle ADC. Segment AC is drawn with a perpendicular, DB. We are given that AC has a length of 16 units.
```
A-----C
| |
D-|-----B
|
```
2. Since AD and DC are radii of the circle, they are equal in length. Let's call this length x.
3. Now, we have a right triangle ADC with sides AD, DC, and AC. Using the Pythagorean theorem, we can relate the lengths of these sides:
AC^2 = AD^2 + DC^2
(16)^2 = x^2 + x^2 [since AD = DC = x]
256 = 2x^2
4. Simplifying the equation, we divide both sides by 2:
x^2 = 128
5. To find the value of x, we can take the square root of both sides:
x = √(128)
6. Simplifying the square root of 128, we get:
x ≈ 11.31
7. Since CB is equal to DC, which is x, the length of CB is approximately 11.31 units.
Therefore, the length of CB is approximately 11.31 units.