Circle Theorems Calculator
Apply circle theorems to solve geometric problems with angles, chords, secants, and tangents
Select Circle Theorem
Inscribed Angle Theorem
θᵢ = θc / 2 (Inscribed angle is half the central angle)
Results
Calculated Central Angle: 0.00 °
Calculated Inscribed Angle: 0.00 °
Arc Length: 0.00 units
Formula: θᵢ = θc / 2
Circle Theorems
Inscribed Angle
Half the central angle
Thales
Semicircle = 90°
Cyclic Quad
Opposite angles = 180°
Chords
Equal distance = equal length
Secants
Power of a point
Tangent
Perpendicular to radius
Formula Reference
Inscribed Angle:
θᵢ = θc / 2
Cyclic Quadrilateral:
∠A + ∠C = 180°
Chord Distance:
r² = (c/2)² + d²
Secants:
PA · PD = PB · PC
Tangent Slope:
m = -x/y
Understanding Circle Theorems
What are Circle Theorems?
Circle theorems are geometric principles that describe relationships between angles, lines, and arcs in circles. These theorems are fundamental tools for solving geometric problems and understanding circular geometry.
Key Applications
- •Solving for unknown angles in circles
- •Finding chord lengths and distances
- •Proving geometric relationships
- •Constructing tangent lines
Important Concepts
Inscribed vs Central Angles
An inscribed angle is always half the central angle that subtends the same arc.
Cyclic Quadrilaterals
In any quadrilateral inscribed in a circle, opposite angles are supplementary (sum to 180°).
Power of a Point
For secants from an external point, the products of segment lengths are equal.
Study Tips
Visual Learning
Draw diagrams to visualize the relationships between angles and lines.
Practice
Work through multiple examples to recognize pattern applications.
Memorize Key Formulas
Learn the fundamental relationships to solve problems quickly.