Circular Arc Tangent Calculator

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Understanding Circular Arc Tangents

Basic Principles

d = √[(x₂-x₁)² + (y₂-y₁)²]

θ = arccos(r/d)

where d is distance, r is radius, θ is tangent angle

Fundamental Properties

  • Perpendicularity at tangent point
  • Equal tangent lengths
  • Right angle theorem
  • Power of a point
  • Circle inversion

Applications

  • Engineering design
  • Computer graphics
  • Path planning
  • Mechanical systems
  • Optical design

Advanced Topics

Geometric Theorems

  • Apollonian circles
  • Radical axis
  • Pole and polar
  • Homothety
  • Circle bundles

Real-world Applications

  • CAD/CAM systems
  • Robotics
  • Computer vision
  • Manufacturing
  • Architecture