Properties of Chords

Perpendiculars from Centre to Chords

Perpendicular Bisector of a Chord

Chord Length and Distance from Centre

Problem 1

Problem 2

Arcs, angles and chords

Relations

Properties of Angles in a Circle

Angle at the Circumference

Angle at the Centre is twice the Angle at the Circumference subtended by the same arc

Arcs are proportional to Angles at Circumference (Centre)

Angle in a semi-circle

Angle in a segment

Angles in the same segment

Problem 1

Problem 2

Problem 3

Cyclic Quadrilaterals

Opposite Angles of Cyclic Quadrilateral

Exterior Angles of Cyclic Quadrilateral

Problem 1

Problem 2

Problems 3

Tests for Concyclic Points

Converse of "Angles in the Same Segment"

Exterior Angles of Cyclic Quadrilateral

Tangents to a Circle

Tangent is perpendicular to the Radius at the Point of Contact

Tangent-Chord Angle

Angles in Same/Alternate Segments

Tangents from an external points