Integrated Math 2 / Unit 8: Circles
8.1 Central and Inscribed Angles
Notes
A central angle has its vertex at the center. An inscribed angle has its vertex on the circle.
- A central angle equals its intercepted arc.
- An inscribed angle equals half its intercepted arc.
- An angle inscribed in a semicircle is a right angle ($90°$).
- Example: an inscribed angle that intercepts a $110°$ arc measures $55°$.
Practice
An inscribed angle intercepts an arc of $110°$. What is the angle's measure?
An inscribed angle is half its intercepted arc.
A central angle measures $72°$. What is the measure of its intercepted arc?
A central angle has the same measure as its arc.
An inscribed angle intercepts a diameter. What is its measure?
A diameter cuts a $180°$ arc, and half of that is $90°$.
Ready for more? Take the Unit 8 test.