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 relationship in circle geometry helps solve many geometric problems involving circles.

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

Explanation: The calculator can find either the inscribed angle or the intercepted arc when one is known, or verify if given values satisfy the theorem.

3. Importance of Inscribed Angles

Details: Understanding inscribed angles is crucial for solving circle geometry problems, analyzing cyclic quadrilaterals, and working with central angles.

4. Using the Calculator

Tips: Enter either the inscribed angle or the intercepted arc (leave the other field empty). The calculator will compute the missing value. Values must be between 0-180° for angles and 0-360° for arcs.

5. Frequently Asked Questions (FAQ)

Q1: What's the difference between central and inscribed angles?
A: A central angle has its vertex at the circle's center and equals its intercepted arc. An inscribed angle has its vertex on the circle and equals half its intercepted arc.

Q2: Can an inscribed angle be more than 180°?
A: No, the largest possible inscribed angle is 180° (which intercepts a semicircle).

Q3: What if two inscribed angles intercept the same arc?
A: They are congruent (equal in measure).

Q4: Does this work for angles formed by tangents and chords?
A: Yes, the angle formed by a tangent and chord equals half its intercepted arc.

Q5: How is this used in real-world applications?
A: Inscribed angles are used in engineering, architecture, and navigation where circular designs or measurements are involved.