A circle is a perfectly round geometric shape which you will see again and again in your studies of math concepts. You will need to have an understanding of its diameter, radius, circumference, area, arcs, and sectors. You will also work with objects that are tangent to a circle and deal with their properties in context.
All the points on a circle are at an equal distance from the center. If you think as a perfectly round pie as a circle, each point on the border represents an endpoint. When you slice a pie from one end of the border to the other, you form a chord.
You should be able to determine the radius from the diameter and vice versa.
Imagine that you want to find the distance around the border of the pie or circle. This measurement is called the circumference. To find out how much space is inside of the border of pie, we could measure the area of the circle. The circumference and the area can be calculated by using the information provided about the radius or diameter.
Let’s say we want to take a slice of the pie from the center. This would form a sector with a corresponding arc length. The sector area and arc the length of these slices vary depending on the size of the slice of pie.To help remember the formula for sector area, remember that it looks very similar to the equation for the area of a circle (A = πr2).
Likewise, the formula for arc length is very similar to the equation for the circumference (C = 2πr). The only difference is that we plug in the ratio of the central angle formed from the two radii intersecting at the center of the sector vs. the angle measure of a circle (360°) into each respective equation.
If we wanted to get creative with how we slice our pie by making diagonal cuts at each endpoint until we form a triangle, we would form an inscribed angle. Keep in mind that the lines from endpoint to endpoint would make up the chords of the circle. This would differ from the central angle formed when the pie was sliced from the center in the previous example. Geometrically, the measure of the inscribed angle is half that of the central angle.
If we lay down a straight line that touches the pie at a single point, the line is considered to be tangent to the circle.
Answers to Practice Problems