1. Central and Inscribed Angles

A central angle is an angle whose vertex is at the center of a circle and whose sides (rays) extend to the circumference. An inscribed angle is an angle whose vertex lies on a circle and whose sides contain chords of the circle.

2. How the Calculator Works

The calculator uses the fundamental relationship between central and inscribed angles:

This relationship holds true when both angles subtend the same arc of the circle.

3. Geometric Relationship

Details: The central angle is always twice the measure of the inscribed angle that subtends the same arc. This is a fundamental theorem in circle geometry.

4. Using the Calculator

Tips: Enter either the central or inscribed angle (0-360 degrees), select which type of angle you entered, and the calculator will compute the other angle.

5. Frequently Asked Questions (FAQ)

Q1: Does this relationship always hold?
A: Yes, as long as both angles subtend the same arc of the circle.

Q2: What if the inscribed angle doesn't pass through the center?
A: The relationship still holds as long as both angles subtend the same arc.

Q3: Can this be used for angles greater than 180 degrees?
A: Yes, though such angles would represent major arcs.

Q4: How does this relate to arc measure?
A: The central angle's measure equals the measure of its intercepted arc.

Q5: Are there exceptions to this rule?
A: No, this is a fundamental geometric theorem with no exceptions.