PEAZIT Aha card
Go straight to resources ↓An inscribed angle is half the central angle
An inscribed angle has its vertex on the circle. It is half the central angle for the same intercepted arc, which excludes its vertex.
| Relation | Meaning |
|---|---|
| α = 2β | The central angle is twice as large. |
| α = 100° | The selected arc has central angle 100°. |
| β = 100° / 2 = 50° | Halve it for the inscribed angle. |
One worked example
- α = 2βThe central angle is twice as large.
- α = 100°The selected arc has central angle 100°.
- β = 100° / 2 = 50°Halve it for the inscribed angle.
Watch out: Matching endpoints alone are insufficient: select the correct arc. An angle in a semicircle is 90°.
Goal, prerequisites and card origin
What you will learn: Connect central and inscribed angles.
What you need first: Circles, angles and halving.
An original PEAZIT working card. Independent expert review and effectiveness testing have not yet taken place. · v1
Show connections
An inscribed angle has its vertex on the circle. It is half the central angle for the same intercepted arc, which excludes its vertex.