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 intercept.

2. How the Calculator Works

The calculator uses the Inscribed Angle Theorem formula:

The calculator can work in both directions:

• Calculate the inscribed angle when you know the intercepted arc
• Calculate the intercepted arc when you know the inscribed angle

3. Practical Applications

Geometry Problems: This theorem is essential for solving many circle geometry problems, including finding unknown angles and arcs in complex diagrams.

Real-world Applications: Used in engineering designs involving circular components, architecture, and navigation systems.

4. Using the Calculator

Steps:

1. Select whether you want to calculate the angle or the arc
2. Enter the known value in degrees
3. Click "Calculate" to get the result

5. Frequently Asked Questions (FAQ)

Q1: What is an inscribed angle?
A: An angle formed by two chords in a circle that have a common endpoint on the circle.

Q2: What is an intercepted arc?
A: The arc that lies between the two chords forming the inscribed angle.

Q3: Does the theorem work for all inscribed angles?
A: Yes, as long as the angle's vertex is on the circle and its sides are chords of the circle.

Q4: What if the angle is at the center of the circle?
A: Then it's a central angle, which equals the measure of its intercepted arc (not half).

Q5: Can this be used for angles formed by tangents?
A: No, this theorem specifically applies to angles formed by two chords. Tangents follow different rules.