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 an intercepted arc on the circle.

2. How Does the Calculator Work?

The calculator uses the inscribed angle theorem:

Where:

• Inscribed Angle — The angle formed inside the circle (degrees)
• Arc — The intercepted arc opposite the angle (degrees)

Explanation: The measure of an inscribed angle is half the measure of its intercepted arc.

3. Importance of Inscribed Angles

Details: Understanding inscribed angles is fundamental in circle geometry, helping solve problems involving cyclic quadrilaterals, tangent lines, and arc measures.

4. Using the Calculator

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

5. Frequently Asked Questions (FAQ)

Q1: What's the relationship between inscribed and central angles?
A: A central angle is equal to its intercepted arc, while an inscribed angle is half of its intercepted arc.

Q2: What if the arc is more than 180 degrees?
A: The calculator works for any arc measure between 0-360 degrees. The inscribed angle will be between 0-180 degrees.

Q3: Do all inscribed angles intercepting the same arc have the same measure?
A: Yes, all inscribed angles that intercept the same arc are equal in measure.

Q4: What's special about an inscribed angle that intercepts a semicircle?
A: An inscribed angle intercepting a semicircle (180° arc) is always a right angle (90°).

Q5: Can this be used for angles formed by tangents and chords?
A: The angle formed by a tangent and chord is also half its intercepted arc, so the same formula applies.