Circle Language, Chords and Perpendicular Bisectors

Circle Language, Chords and Perpendicular Bisectors

Circle geometry starts with precise language: a radius joins centre to circumference, a diameter passes through centre, a chord joins two circumference points, and a tangent touches once. The perpendicular from the centre to a chord bisects the chord, and the perpendicular bisector of a chord passes through the centre. State a named theorem when writing a proof.

Worked reasoning

If a radius is perpendicular to a chord, it cuts the chord into two equal lengths. A 12 cm chord is split into 6 cm and 6 cm.

Exam method

1. Mark given equal radii/tangent or chord facts. 2. Identify the relevant circle theorem. 3. Write the reason beside each conclusion.

Geometry proofs need reasons

A proof answer should pair every new statement with a reason: equal radii, radius perpendicular to tangent, perpendicular from centre to chord, or definition of a diameter. Do not rely on a diagram being drawn to scale. If a fact is not marked, stated or proved, it is not yet available. Reproduce a simple annotated circle from memory and practise writing a two-column flow of statement and reason; this is the language expected in formal geometry questions.

One-minute retrieval: Circle Language, Chords and Perpendicular Bisectors

Close the worked solution. From memory, state its central rule, name one condition that makes it valid, and reconstruct one check that would catch a typical exam error.