Angles at Centre & Circumference Flashcards

All 4 cards in this deck

State the circle theorem about the angle at the centre.

The angle at the centre is twice the angle at the circumference when both are subtended by the same arc.

What does it mean to say two angles are 'subtended by the same arc'?

e.g. $\angle AOB$ and $\angle ACB$

Both angles are formed by lines drawn to the same two endpoints of that arc.

e.g. both stand on arc $AB$.

Does the 'angle at the centre' theorem still work when the angle at the centre is reflex?

Yes — the reflex angle at the centre is twice the angle at the circumference in the opposite segment.

True or false? Any angle at the centre of a circle is twice any angle at the circumference.

False. The two angles must be subtended by the same arc (stand on the same chord).