1. What is the Inscribed Angle of Circle?

The Inscribed Angle of Circle is the angle formed in the interior of a circle when two secant lines intersect on the Circle. It is an important concept in circle geometry that relates to arc lengths and central angles.

2. How Does the Calculator Work?

The calculator uses the Inscribed Angle formula:

Where:

• \( \pi \) — Archimedes' constant (approximately 3.14159)
• \( lArc \) — Arc Length of Circle (meters)
• \( r \) — Radius of Circle (meters)

Explanation: The formula calculates the inscribed angle based on the relationship between the arc length and the radius of the circle.

3. Importance of Inscribed Angle Calculation

Details: Calculating inscribed angles is crucial in geometry for solving circle-related problems, designing circular structures, and understanding angular relationships in circular motion.

4. Using the Calculator

Tips: Enter arc length and radius in meters. Both values must be positive numbers greater than zero for accurate calculation.

5. Frequently Asked Questions (FAQ)

Q1: What is the relationship between inscribed angle and central angle?
A: An inscribed angle is half the measure of the central angle that subtends the same arc.

Q2: Can the inscribed angle be greater than 90 degrees?
A: Yes, inscribed angles can range from 0 to 180 degrees (0 to π radians), depending on the arc length and radius.

Q3: What are the units for the calculated angle?
A: The calculator returns the angle in radians, which is the standard unit for angular measurement in mathematics.

Q4: How does the radius affect the inscribed angle?
A: For a given arc length, a larger radius will result in a smaller inscribed angle, and vice versa.

Q5: Can this formula be used for any circle?
A: Yes, this formula applies to all circles regardless of size, as long as the arc length and radius are known.