Circle theorems explorer

<p>A chord joins two points on a circle. A diameter is a chord through the centre. Radii of the same circle are equal.</p>
<p>The perpendicular from the centre \(O\) to a chord \(AB\) bisects the chord. For a non-diameter chord, the line from the centre to its midpoint is perpendicular to it.</p>
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<p>In the diagram, \(AM=MB\) and \(\angle OMA=90^\circ\). Use the right triangle \(OMA\) when finding a chord length or its distance from the centre.</p>
<p>In the same circle, or circles of equal radius, equal chords are equidistant from the centre. These distances are perpendicular distances. Equal chords also subtend equal minor angles at the centre.</p>

A chord joins two points on a circle. A diameter is a chord through the centre. Radii of the same circle are equal.

The perpendicular from the centre \(O\) to a chord \(AB\) bisects the chord. For a non-diameter chord, the line from the centre to its midpoint is perpendicular to it.

In the diagram, \(AM=MB\) and \(\angle OMA=90^\circ\). Use the right triangle \(OMA\) when finding a chord length or its distance from the centre.

In the same circle, or circles of equal radius, equal chords are equidistant from the centre. These distances are perpendicular distances. Equal chords also subtend equal minor angles at the centre.

Chords and the centre

Chords and the centre