What you’ll learn
Understand inscribed angles.
Key idea
Chord sides and a circumference vertex define an inscribed angle, which measures half the intercepted arc.
The intercepted arc excludes the angle vertex; its inscribed angle is half its degree measure.
Worked example
Classify examples and non-examples for the concept 'Understand inscribed angles'.
Circle O has radius 3; A/B bound a minor arc of 160 degrees, and P is a distinct point on the complementary major arc. Chords PA and PB form angle APB. Classify APB with defining evidence.
- P lies on the circumference, not at the center; both sides are chords.
- APB intercepts the minor arc not containing P; its measure is 160/2=80 degrees.
Answer: Inscribed angle — its vertex lies on the circle and both sides meet other circle points.
Quick Check
Classify examples and non-examples for the concept 'Understand inscribed angles'.
Circle O has radius 7; A/B bound a minor arc of 20 degrees, and P is a distinct point on the complementary major arc. Chords PA and PB form angle APB. Classify APB with defining evidence.