Angle Relationships in Circles

Explore the fascinating relationships between tangents, radii, and angles in circle geometry

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📐 Proof Steps

Select an example to see the mathematical proof
Welcome to Angle Relationships in Circles! Discover the elegant connections between tangents, radii, and angles.
📐 Tangent-Radius Angle Theorem

When two tangents are drawn from an external point, the angle between them relates to angles formed with radii. This creates beautiful isosceles triangles.

∠PTQ = 2∠OPQ
🔺 Inscribed Angle Theorem

An inscribed angle is half the central angle that subtends the same arc. This fundamental relationship appears throughout circle geometry.

Inscribed Angle = ½ Central Angle
⭕ Central Angle Properties

Central angles provide the foundation for measuring arcs and relating to inscribed angles. They create direct arc-angle correspondences.

Central Angle = Arc Measure
🌙 Angle-Arc Relationships

Various angle types in circles have specific relationships to the arcs they intercept, creating a unified framework for circle geometry.

Different angle types = Different arc ratios