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

1

Inscribed Angle

Half the central angle

2

Thales

Semicircle = 90°

3

Cyclic Quad

Opposite angles = 180°

4

Chords

Equal distance = equal length

5

Secants

Power of a point

6

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.