1. What is an Inscribed Angle?

An inscribed angle is an angle formed by two chords in a circle which have a common endpoint. This common endpoint forms the vertex of the inscribed angle. The other two endpoints define what we call an intercepted arc on the circle.

2. How Does the Calculator Work?

The calculator uses the inscribed angle formula:

Where:

• \( \text{side} \) — Length of the chord (units)
• \( \text{radius} \) — Radius of the circle (units)
• \( \arcsin \) — Inverse sine function

Explanation: The formula calculates the angle whose sine equals the ratio of half the chord length to the radius, then converts from radians to degrees.

3. Geometric Relationships

Details: The inscribed angle theorem states that an angle θ inscribed in a circle is half of the central angle 2θ that subtends the same arc on the circle.

4. Using the Calculator

Tips: Enter the chord length and circle radius in consistent units. The chord length must be ≤ diameter (2×radius) for valid results.

5. Frequently Asked Questions (FAQ)

Q1: What's the relationship between chord length and angle?
A: Longer chords (up to diameter) correspond to larger inscribed angles, with maximum 90° when chord equals diameter.

Q2: Can this calculate chord length from angle?
A: No, this calculator specifically finds the angle from chord length and radius.

Q3: What units should I use?
A: Any consistent units (cm, inches, etc.) as long as both measurements use the same unit.

Q4: Why does my calculation show no result?
A: This happens if chord length exceeds diameter (2×radius), which is geometrically impossible.

Q5: How accurate are the results?
A: Results are mathematically precise, though displayed with 2 decimal places for readability.