Circle Theorems Calculator
Calculate angles using various circle theorems and relationships.
Results
Result Angle
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Theorem Applied
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Explanation
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Circle Theorems Guide
Circle theorems are fundamental relationships between angles, chords, tangents, and arcs in circles. Understanding these theorems is essential for solving geometry problems.
1. Inscribed Angle Theorem
An inscribed angle is half the measure of the central angle that subtends the same arc. Formula: Inscribed Angle = Central Angle ÷ 2
2. Central Angle Theorem
A central angle is twice the measure of any inscribed angle that subtends the same arc. Formula: Central Angle = Inscribed Angle × 2
3. Cyclic Quadrilateral Theorem
In a cyclic quadrilateral (inscribed in a circle), opposite angles are supplementary. Formula: Angle A + Angle C = 180°, Angle B + Angle D = 180°
4. Tangent-Radius Theorem
A tangent to a circle is perpendicular to the radius at the point of contact. The angle between a tangent and radius is always 90°.
5. Equal Chords Theorem
Equal chords in a circle subtend equal angles at the center and equal inscribed angles. If two chords are equal in length, their corresponding central and inscribed angles are also equal.
Note: These theorems are fundamental in circle geometry and are widely used in mathematics, engineering, and design. All angle measurements are in degrees.
This calculator provides mathematical calculations based on standard circle theorems. Results are for educational and informational purposes. While we strive for accuracy, please verify important calculations independently.