- 1. The Perpendicular Bisector of a Chord
State the theorem that the perpendicular bisector of a chord passes through the centre, and use the right-angled triangle it creates — radius, perpendicular distance and half-chord — with Pythagoras' theorem to find a chord length, the distance of a chord from the centre, or the radius, including two-chord problems in the same circle.
- 2. Equal Chords are Equidistant from the Centre
State and prove that equal chords of a circle are equidistant from the centre, apply the converse that chords equidistant from the centre are equal, and combine the two with Pythagoras' theorem to solve numerical, parallel-chord, and diagram-based problems.
- 3. Angles Subtended by Equal Chords
State and apply the theorem that equal chords of a circle subtend equal angles at the centre, use its converse, relate equal chords to equal arcs, and connect the result to the angle-at-the-centre-is-twice-the-angle-at-the-circumference relationship.
- 4. Combining the Chord Properties
Combine the perpendicular-bisector, equal-distance, and equal-angle chord results to solve multi-step problems, including parallel chords (adding or subtracting distances) and the common chord of two intersecting circles, for both equal and unequal circles.
- 5. Chord Properties in Exam Practice
Identify which chord property a problem needs, read an exam diagram, and solve full WAEC/JAMB-style questions — finding the angle a chord subtends at the centre, the length of a chord from its central angle, and the arc length or perimeter of the minor segment a chord cuts off.
