Four points, \(A, B, C,\) and \(D,\) lie on a circle having a circumference of 17 units. \(B\) is 5 units counter clock wise from \(A . C\) is 3 units clockwise from \(A . D\) is 11 units clockwise from \(A\) and 6 units counterclockwise from \(A\) . What is the order of the points, starting with \(A\) and going clockwise around the circle? E. \(A, B, C, D\) G. \(A, B, D, C\) H. \(A, C, B, D\) J. \(A, C, D, B\) K. \(A, D, C, B\)

Geometry is a branch of mathematics that deals with the properties, measurements, and relationships of points, lines, angles, surfaces, and solids. For the ACT Math test, a solid understanding of geometry principles is crucial. Specifically, working with circles requires understanding their various components, such as radius, diameter, and circumference.

When dealing with circle problems on the ACT, you need to be comfortable with common geometric terms and how they apply within the context of a problem. In the given exercise, we had to use the geometric property that points around a circle can be described by their position relative to each other, often in terms of the distance along the circle's edge.

The circumference is the total distance around a circle. It's equivalent to the perimeter of a circle and is calculated using the formula \( C = 2\pi r \), where \( C \) is the circumference and \( r \) is the radius of the circle. For the ACT, understanding this concept is vital, especially when we're given dimensions related to the circle that need to be used in problem-solving.

Knowing the circumference allows us to determine how far points on a circle are from each other when moving along the edge of the circle. In our exercise, the circumference was given as 17 units which was a key piece of information to solve the problem.

A circle is a two-dimensional shape where all points are an equal distance from the center. The distance around a circle is called the circumference, and the line segment from the center of the circle to any point on the circle is the radius. A line segment that crosses the circle and has endpoints on the circle is called a diameter, and it's twice as long as the radius.

In our exercise, understanding that the distance a point has traveled along the circumference can be calculated clockwise or counterclockwise is essential. If a point has moved counterclockwise from point A, you can find the clockwise measurement by subtracting the counterclockwise distance from the total circumference.

ACT problem-solving involves applying mathematical concepts to answer questions effectively. The key is to understand the information given, break down the problem into manageable parts, and use logical reasoning to eliminate incorrect answer choices.

In the given exercise, we applied these steps by interpreting the positions of the points on the circle and understood how to use the circumference to find the points' order. Recognizing that the clockwise and counterclockwise measurements relate to the circle's total circumference was crucial. By eliminating answer choices that did not match the determined order, we could arrive at the correct answer. This process of elimination is a powerful tool in the ACT Math section and can save time and increase accuracy.