Inscribed Angle Calculator - Circle Geometry Solver
Calculate inscribed angles, central angles, and intercepted arcs using the Inscribed Angle Theorem. Solve circle geometry problems and Thales' Theorem online.
Solving circle geometry problems is significantly easier with our Inscribed Angle Calculator. Follow these steps to find missing angular measurements:
Step 1: Identify the components of your circle. An 'Inscribed Angle' is an angle formed by two chords that meet at a vertex on the circle's edge. The 'Intercepted Arc' is the section of the edge between the two chords.
Step 2: Enter your known value. You can provide the 'Measure of the Inscribed Angle' (in degrees) to find the arc, or enter the 'Measure of the Intercepted Arc' to find the angle.
Step 3: (Optional) If you have the 'Central Angle' (an angle starting at the center), you can enter that instead.
Step 4: Click the 'Calculate' button.
Step 5: Review the results. The calculator will provide the missing values and explain the theorem used.
Step 6: Use the visual diagram to confirm that the vertex of your angle is correctly positioned on the circumference, as moving it toward the center changes the mathematical relationship entirely.
The calculator relies on the 'Inscribed Angle Theorem,' a core principle of Euclidean geometry.
1. Angle-to-Arc: The measure of an inscribed angle is exactly HALF the measure of its intercepted arc. Formula: Inscribed Angle = ½ × Intercepted Arc.
2. Central Angle Relationship: Because a central angle is equal to its intercepted arc, an inscribed angle is also exactly half of the central angle that intercepts the same arc.
Example: If you have an intercepted arc of 100 degrees, the inscribed angle formed by those same two points will be exactly 50 degrees. If the inscribed angle is 90 degrees, the arc must be 180 degrees (a semicircle).
The Inscribed Angle Calculator is a specialized tool for students and professionals working in trigonometry and mechanical design. Circle theorems are more than just school exercises; they are used in civil engineering to design curved roads and in astronomy to calculate the positions of celestial bodies based on observed arcs. One of the most famous corollaries of this theorem is Thales's Theorem, which states that any angle inscribed in a semicircle is always a right angle (90°). Our tool ensures you never mix up the 'half' vs 'equal' relationship, providing instant verification for complex geometric proofs.
Verified Precise