Detailed definition
Understanding Semicircle
A semicircle is half of a circle, determined by a diameter. In angle language it corresponds to a 180-degree arc, and in region language it describes one of the two equal halves formed by the diameter.
Semicircles are important in theorem work because an angle inscribed in a semicircle is a right angle. That makes diameter-based diagrams especially valuable in circle geometry.
This page keeps the diameter visible so the semicircle is read from its defining cut, not from a vague half-round picture.
Key facts
Important ideas to remember
- A semicircle is half of a circle and spans 180 degrees.
- A semicircle is determined by a diameter, not by any random chord.
- The arc of a semicircle measures 180 degrees.
- A point on the semicircle connected to the diameter's endpoints forms a right inscribed angle.
Where it is used
Where semicircle shows up
- Use semicircles in Thales-type right-angle problems.
- Use them when finding half-circle area, arc length, or perimeter relationships.
- Use them in diagrams where diameter creates two equal circular parts with different theorem consequences.
Common mistakes
What to watch out for
- Do not call a region a semicircle unless the dividing line is a diameter.
- Do not confuse a semicircle with a general segment region that only looks cap-shaped.
- Do not ignore whether the problem means the 180-degree arc or the half-disk region.