### Calculations with Diameter

You will remember that the diameter of a circle is two times the radius.

This is a very basic concept since the computation merely involves multiplying by two.

Therefore, it is unlikely that you would see a very simple computation like this on the exam.

### Diameter and Tangency – Practice Problem

Have a look at the problem below, in which you have to do a calculation based on coordinate geometry concepts.

If a circle with center (−6, 6) is tangent to the *x* axis in the standard (*x*, *y*) coordinate plane, what is the diameter of the circle?

A. −6

B. −12

C. 6

D. 12

E. 36

**The correct answer is D.**

Remember that if the center of a circle (*x*, *y*) is tangent to the *x* axis, then both of the following conditions are true:

(1) The point of tangency is equal to (*x*, 0).

AND

(2) The distance between (*x*, *y*) minus (*x*, 0) is equal to the radius.

The center of this circle is (−6, 6) and the point of tangency is (−6, 0).

So, we need to subtract these two coordinates in order to find the length of the radius:

(−6, 6) − (−6, 0) = (0, 6)

In other words, the radius length is 6.

Also remember this formula:

diameter length = radius length × 2 =

6 × 2 =

12

So, you will also need to know how to calculate diameter itself using the facts stated in more advanced math problems like the above.

You will also need to know how to use diameter to calculate the circumference or area of a circle for geometry problems on the exam.

So, normally you would need to calculate diameter to work out the solution to other problems.

If you have not already done so, you should have a look at our page on **circumference**.

Go back to the **Geometry Exercises Page**.

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