Circle Theorems (Leaving Cert Mathematics): Flashcards

Products of segments of each chord are equal

$AP \times PB = CP \times PD$

Similarity of triangles formed by intersecting chords

$90°$ (right angle)

Diameter subtends semicircle, forms right triangle with radii

Supplementary

$180°$

Opposite arcs form full circle ($360°$)

Perpendicular at point of contact

Tangent touches circle at exactly one point

Angle between tangent & chord = angle in alternate segment

Angles subtended by chord in different segments are equal