This tool calculates the measure of an inscribed angle in a circle based on the arc it intercepts.

## How to Use the Inscribed Angle Calculator

Enter the coordinates for the center of the circle (cx, cy), one point on the circumference you are measuring from (px, py), and the two points on the arc (qx, qy) and (rx, ry). Click “Calculate” to get the inscribed angle.

## How It Calculates the Results

The calculator uses the formula for the inscribed angle where the angle is formed by two chords in a circle that have a common endpoint. The angle is calculated using trigonometric functions to find the angular displacement between the two chords.

## Limitations

The calculator assumes a perfect circle and does not account for any distortions or irregularities in the shape of the circle. Ensure the entered points are accurate and in a consistent coordinate plane.

## Use Cases for This Calculator

### Calculate inscribed angle when radius and arc length are known

Enter the values for radius and arc length to find the inscribed angle. This use case is helpful when you have the radius and arc length and want to quickly determine the inscribed angle formed by the arc.

### Determine the inscribed angle using radius and chord length

Provide the radius and chord length to compute the inscribed angle. This feature is useful when you have the radius and chord length and need to find the corresponding inscribed angle effortlessly.

### Find the inscribed angle based on the diameter and arc length

Input the diameter and arc length to calculate the inscribed angle. This use case enables you to determine the central angle subtended by the arc using the diameter and arc length values.

### Calculate inscribed angle using diameter and chord length

Enter the diameter and chord length to determine the inscribed angle. This function allows you to quickly find the inscribed angle formed by the chord with the given diameter.

### Compute inscribed angle with circumcircle radius and chord length

Input the circumcircle radius and chord length to find the inscribed angle. Use this feature when you have the circumcircle radius and chord length and need to calculate the inscribed angle accurately.

### Calculate inscribed angle when circumcircle radius and arc measure are given

Provide the circumcircle radius and arc measure to compute the inscribed angle. This use case helps you find the inscribed angle when you have the circumcircle radius and arc measure of the circle.

### Determine inscribed angle using circumcircle radius and sector area

Input the circumcircle radius and sector area to find the inscribed angle. Use this feature to quickly determine the inscribed angle based on the given circumcircle radius and sector area.

### Find inscribed angle with triangle side lengths

Enter the lengths of the sides of the triangle enclosing the circle to calculate the inscribed angle. This use case allows you to find the inscribed angle by considering the triangle formed by the circle’s center and two points on the circle.

### Determine central angle with inscribed angle and chord length

Input the inscribed angle and chord length to calculate the central angle. This function helps you find the central angle subtended by the chord in the circle using the inscribed angle and chord length.

### Calculate inscribed angle using any combination of available parameters

Feel free to mix and match any known parameters to quickly find the inscribed angle. This versatile calculator allows you to input various combinations of values for efficient calculation of the inscribed angle in different scenarios.