1. What is the Inscribed Angle Theorem?

The Inscribed Angle Theorem states that an angle inscribed in a circle is half the measure of its intercepted arc. This fundamental geometric principle relates angles and arcs in circle geometry.

2. How Does the Calculator Work?

The calculator uses the Inscribed Angle Theorem:

Where:

• Inscribed Angle — The angle formed by two chords in a circle that have a common endpoint
• Arc Between Points — The arc of the circle that lies between the other two endpoints of the chords

Explanation: The theorem shows the direct proportional relationship between an inscribed angle and its intercepted arc.

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: Enter the measure of the arc between points in degrees (must be between 0 and 360). The calculator will compute the measure of the inscribed angle that intercepts that arc.

5. Frequently Asked Questions (FAQ)

Q1: Does the position of the angle affect the theorem?
A: No, as long as the vertex is on the circle and the sides are chords, the theorem applies regardless of the angle's position.

Q2: What if the angle is at the center of the circle?
A: A central angle equals the measure of its intercepted arc (not half). This is a different case from an inscribed angle.

Q3: Can the arc measure be more than 180 degrees?
A: Yes, but the inscribed angle will always be ≤ 90° because it's half of the smaller arc between the points.

Q4: How does this relate to Thales' theorem?
A: Thales' theorem is a special case where the inscribed angle is 90° and the intercepted arc is 180° (a semicircle).

Q5: Can this be used for angles formed by tangents?
A: No, this calculator is specifically for angles formed by two chords. Tangents require different formulas.