Chords – Solving Master

Perpendicular line from the centre to chord bisects chord.

Condition: $ON\perp AB$

Result: $AN=BN$

Reference: $\perp$ line from centre to chord bisects chord
Line joining the centre to the mid-point of chord is perpendicular to chord.

Condition: $AM=MB$

Result: $OM\perp AB$

Reference: line joining centre and mid-pt of chord $\perp$ chord
The perpendicular bisector of a chord passes through the centre.

Reference: $\perp$ bisector of chord passes through centre
For two equal chords, their distances from the centre are equal.

Condition: $AB=CD$

Result: $OM=ON$

Reference: eq. chords equidistant from centre
For two chords are equidistant from the centre, they are equal in length.

Condition: $OM=ON$

Result: $AB=CD$

Reference: chords equidistant from centre eq.