lesson
Tangent-Radius Perpendicularity Theorem
Prove that a line is tangent to a circle if and only if it is perpendicular to the radius drawn to the point of tangency.
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Circle Theorems, Tangents, and Inscribed Angles
9 lessons
Goal
Prove and apply theorems regarding central angles, inscribed angles, chords, tangent lines, and cyclic quadrilaterals.
9 lessons
0 of 9 done
- Circle Definitions: Central Angles and Arc MeasuresUp next
- Inscribed Angle Theorem and CorollariesNot started yet
- Perpendicular Bisector of a Chord Theorem and ProofNot started yet
- Equidistant Chords and Congruent ArcsNot started yet
- Tangent-Radius Perpendicularity TheoremYou are here
- Tangent Segments from an External Point TheoremNot started yet
- Circumscribed Angles and Inscribed Circle RelationshipsNot started yet
- Inscribed Quadrilaterals and Opposite Angle SupplementarityNot started yet
- Angles Formed by Tangents, Secants, and ChordsNot started yet
Learning standards covered
OGM.9.GEO.5Open Global Math Standards 2026™ · 8th GradeUnderstand and apply the properties of circles (central angles, inscribed angles, chords, perpendicular chord theorem, tangent lines, tangent segments theorem, inscribed/circumscribed polygons, incenter, circumcenter).
OGM.9.GEO.6Open Global Math Standards 2026™ · 8th GradeUnderstand logical proof structures (definitions, propositions, converse, direct proof, proof by contradiction, counterexamples) and construct rigorous synthetic geometric proofs.