Measure arcs, compare chords, and test circle theorems. Switch methods easily across geometric input styles. See clear results, graphs, exports, and worked examples below.
| Method | Input Values | Intercepted Arc | Inscribed Angle | Central Angle |
|---|---|---|---|---|
| Arc Measure | Arc = 120° | 120° | 60° | 120° |
| Central Angle | Central = 88° | 88° | 44° | 88° |
| Chord and Radius | Chord = 10, Radius = 12 | 49.249° | 24.624° | 49.249° |
| Coordinates | O(0,0), A(5,0), B(0,5), C(-5,0) | 180° | 90° | 180° |
Core theorem: Inscribed angle = intercepted arc ÷ 2.
Central-angle form: Inscribed angle = central angle ÷ 2.
Chord-radius form: Chord = 2r × sin(inscribed angle).
Rearranged chord form: Inscribed angle = arcsin(chord ÷ 2r).
An inscribed angle has its vertex on the circle. Its sides intersect the circle at two points and form an intercepted arc. The theorem says the inscribed angle always equals half the measure of that intercepted arc.
When the central angle and the inscribed angle intercept the same arc, the central angle is double the inscribed angle. This makes circle geometry problems much easier to solve.
When you know the chord and the radius, the chord formula gives a direct way to calculate the inscribed angle. This is useful in geometry, drafting, and coordinate-based circle analysis.
With coordinates, the calculator measures angle ABC from vectors BA and BC, then identifies the intercepted arc AC that does not contain the vertex point B.
Step 1: Choose a method. You can solve from an intercepted arc, a central angle, a chord with radius, or full coordinates.
Step 2: Enter the known values. Use degrees for angles and any consistent length unit for radius and chord inputs.
Step 3: Click Calculate Now. The result appears above the form, directly below the header section.
Step 4: Review the computed inscribed angle, intercepted arc, equivalent central angle, and arc length when radius is available.
Step 5: Use the CSV and PDF buttons to export the result summary for class notes, homework checks, or project documentation.
An inscribed angle is an angle whose vertex lies on a circle. Its two sides intersect the circle and define an intercepted arc.
This follows from a standard circle theorem. For the same intercepted arc, the central angle is double the inscribed angle, so the inscribed angle must be half the arc measure.
Yes. Use any consistent unit, such as centimeters, meters, or inches. The angle result stays in degrees, while arc length uses the same length unit you entered.
That input is not valid for a circle. A chord can never exceed the diameter, so the calculator blocks that case and asks for corrected values.
The warning appears when the three entered points are not exactly the same distance from the center. That means the points are not perfectly on one circle, though the calculator can still estimate the result.
The intercepted arc is the arc cut off by the sides of the inscribed angle. In the coordinate method, it is the arc between A and C that does not contain point B.
Yes. If a radius is available, the calculator also finds arc length using the intercepted arc measure and the circle circumference relationship.
It helps with geometry classes, drafting, technical diagrams, coordinate geometry, exam revision, and fast verification of circle-theorem homework or design calculations.
Important Note: All the Calculators listed in this site are for educational purpose only and we do not guarentee the accuracy of results. Please do consult with other sources as well.