# Circumference of a Circle

On this day in 1964 President Johnson signed the Civil Rights Act. Surprisingly, it was met by much opposition from both white and African Americans. Many historians now believe it was a major influence in shaping America's social and political development. You can learn more about the Civil Rights Act here.

## Geometry: Circumference of a Circle

Remember to read the question carefully. Some students panic when they see a complicated diagram. Every problem on the SAT has a solution that you can reach without any particular, specialized knowledge (though you do still need to memorize basic math formulas). Slow down and reread the problem carefully; make sure that you understand what the question is actually asking.

In the figure above, inscribed triangle  is equilateral. If the radius of the circle is , then the length of arc  is

At first, when you look at this diagram it looks quite complicated. You might know some facts about triangles inscribed in circles, but those facts won't help you in this problem. Instead, remember that after you read the problem carefully, you need to identify the "bottom line." You are looking for the length of arc AXB. Note that there is no label that says "figure not drawn to scale." That means that the figure is drawn to scale (in other words, you could make an estimate based on how the figure looks). It does look like the arc AXB is just 1/3 of the circumference of the circle. In fact, if you think about it, it must be (since the triangle is an equilateral triangle). Since you know that the radius of the circle is r, the diameter must be

$2\pi r$
and therefore, the length of arc AXB is just

$\frac{2\pi r}{3}$

Now, take a look at the answers and select the choice that matches your prediction. Don't forget to loop back and verify that your answer matches the "bottom line."

(A)
(B)
(C)
(D)
(E)

The correct answer choice is (A).

On sat.collegeboard.org 54% of the responses were correct.

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