Circles

When a line and circle

When a line and circle are in the same plane, three situations are possible: (1) Non-intersecting line - no common points (2) Secant line - two common

A tangent is a line

A tangent is a line that intersects a circle at exactly one point called the point of contact. Key property: The tangent is perpendicular to the radiu

The number of tangents depends on

The number of tangents depends on point location: (1) Point inside circle: 0 tangents (all lines are secants) (2) Point on circle: exactly 1 tangent (

Theorem 10

Theorem 10.2: Tangent segments drawn from an external point to a circle are equal in length. Step-by-step proof: (1) Draw tangents PQ and PR from exte

When a chord of a larger

When a chord of a larger circle is tangent to a smaller concentric circle, the tangent bisects the chord. Problem-solving approach: (1) Identify the t