1. What is an Inscribed Angle?

An inscribed angle is an angle formed by two chords in a circle which have a common endpoint. This angle is always half the measure of its intercepted arc or the central angle that subtends the same arc.

2. How Does the Calculator Work?

The calculator uses the inscribed angle formula:

Where:

• Central Angle — Angle subtended at the center of the circle (in degrees)
• Inscribed Angle — Angle formed on the circle's circumference (in degrees)

Explanation: The inscribed angle theorem states that an angle inscribed in a circle is half of the central angle that subtends the same arc on the circle.

3. Importance of Inscribed Angle Calculation

Details: Understanding inscribed angles is crucial in geometry for solving problems related to circles, arcs, and cyclic polygons. It's fundamental in many geometric proofs and constructions.

4. Using the Calculator

Tips: Enter the central angle in degrees. The value must be positive and typically between 0° and 360° for circle applications.

5. Frequently Asked Questions (FAQ)

Q1: Does the inscribed angle theorem work for any angle?
A: Yes, as long as the angle is inscribed in a circle and intercepts an arc, the theorem applies.

Q2: What if the central angle is greater than 180°?
A: The formula still applies. The inscribed angle will be half of the central angle, even if it's obtuse.

Q3: Can this be used for angles in radians?
A: The formula works the same way for radians, but this calculator uses degrees by default.

Q4: What's the relationship between inscribed angles and arcs?
A: An inscribed angle is half the measure of its intercepted arc.

Q5: Are all inscribed angles that intercept the same arc equal?
A: Yes, this is known as the Inscribed Angle Theorem Corollary - all angles inscribed in the same arc are equal.