Co-Authored By:

##### Asked by: Gladis Posselt

science space and astronomy# What is the central angle theorem?

Last Updated: 22nd February, 2020

**Theorem**:

**Central Angle Theorem**

**Central Angle Theorem**states that the

**central angle**from two chosen points A and B on the circle is always twice the inscribed

**angle**from those two points. The inscribed

**angle**can be defined by any point along the outer arc AB and the two points A and B.

Click to see full answer.

Keeping this in consideration, what is Centre angle theorem?

**Theorem**: Central **Angle Theorem** The Central **Angle Theorem** states that the central **angle** from two chosen points A and B on the circle is always twice the inscribed **angle** from those two points. The inscribed **angle** can be defined by any point along the outer arc AB and the two points A and B.

why is an inscribed angle half of the central angle? The **inscribed angle** theorem states that an **angle** θ **inscribed** in a circle is **half of the central angle** 2θ that subtends the same arc on the circle. Therefore, the **angle** does not change as its vertex is moved to different positions on the circle.

Accordingly, how do you find a central angle?

Find the **Central Angle** from the Arc Length and Radius You can also use the radius of the circle and the arc length to find the **central angle**. Call the **measure** of the **central angle** θ. Then: θ = s ÷ r, where s is the arc length and r is the radius.

What is the formula of inscribed angle?

By the inscribed angle theorem, the measure of an inscribed angle is half the measure of the intercepted **arc**. The measure of the central angle ∠POR of the intercepted **arc** ?PR is 90°. Therefore, m∠PQR=12m∠POR =12(90°) =45°.