What is a central angle?
Central angle is another or further name for the central angle on a section of a circle. The central angle theorem shows an interesting relationship to the peripheral angle on the circle.
What you need:
- elementary geometry
The central angle - that is what it means
- If you cut a section out of a full circle like a piece of cake, then this circle section (with an arc) will turn out to be larger, the larger it is angle is at the center of the circle.
- Since this angle is in the center of the circle, it will be in the geometry Called the central angle or central angle. The two legs of the angle form the segment of a circle.
- Strictly speaking, there are of course two central angles, because the rest of the circle is also a section of a circle. Both central angles together have 360 °.
The central angle set - simply explained
- There are two simple uses for the central angle. In the first case it describes - as already indicated above - the size of the segment of a circle. It can also be used to calculate the area of this part of the circle; nothing more is required than the angular relationships to the full circle.
- Another interesting geometric relationship concerns the central angle and the associated peripheral angle.
- The peripheral angle is obtained when the circle section is not formed as the center point, but rather the two leg intersection points are connected with a (further) point on the circle. The result is a (mostly) acute triangle with the peripheral angle on the circle.
- Incidentally, the peripheral angle is also called the circumference angle (since its tip lies on the circumference).
- For each central angle, this peripheral angle is always half as large, regardless of how you choose the point on the circumference. The proof of this theorem is longer, of course, but you can draw a few circles and try it out.
Calculate the radius for the section of a circle
A section of a circle can be imagined as a piece of cake made from a ...
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