1. What is the Inscribed Angle Theorem?

The Inscribed Angle Theorem states that the measure of an inscribed angle is half the measure of its intercepted arc. This fundamental theorem in circle geometry relates angles formed by two chords in a circle to the arcs they create.

2. How Does the Calculator Work?

The calculator uses the Inscribed Angle Theorem:

Where:

• Inscribed Angle — Angle formed by two chords in a circle that have a common endpoint
• Intercepted Arc — Arc that lies in the interior of the inscribed angle and has endpoints on the angle

Explanation: The calculator can compute either the inscribed angle or intercepted arc when the other value is known.

3. Importance of Inscribed Angles

Details: Understanding inscribed angles is crucial for solving many geometric problems involving circles, including finding arc measures, chord lengths, and other angle measures in circular diagrams.

4. Using the Calculator

Tips: Select whether you know the inscribed angle or intercepted arc, enter the value in degrees (must be between 0 and 360), and click calculate.

5. Frequently Asked Questions (FAQ)

Q1: Can the intercepted arc be more than 180 degrees?
A: Yes, the intercepted arc can be up to 360 degrees, but the inscribed angle will always be ≤180°.

Q2: What if I know the central angle instead?
A: A central angle equals its intercepted arc, while an inscribed angle is half of its intercepted arc.

Q3: Does this work for angles outside the circle?
A: No, this calculator only works for inscribed angles (vertex on the circle).

Q4: What about angles formed by tangents?
A: Angles formed by a tangent and chord follow a different rule (half the intercepted arc).

Q5: Can I use this for angles in radians?
A: This calculator uses degrees. For radians, convert first (π radians = 180°).