Mathematics — first biennium · Lesson
When a central angle and an inscribed angle intercept the same arc, the inscribed angle is half the central angle.
Prerequisites: Circle elements and angles
Goal: Relate central and inscribed angles intercepting the same arc.
In this lesson: Relate central and inscribed angles intercepting the same arc.
New concept: A central angle has its vertex at the centre of the circle; an inscribed angle has its vertex on the circle. When they subtend the same arc, the inscribed angle is half the central angle.
How to proceed: The key phrase is 'same arc'. Identify A and B, then halve the central angle.
You can already assume: Circle elements and angles.
Central and inscribed angles intercepting the same arc.
Completed exercises: 0/5 · Correct on first attempt: 0
The key phrase is 'same arc'. Identify A and B, then halve the central angle.
Data / situation: In the diagram ∠AOB=120°. Find ∠ACB, which intercepts the same arc AB.
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