Circle theorems explorer

<p>The angle at the centre is twice the angle at the circumference standing on the same arc. Identify the arc before deciding whether the central angle is minor or reflex.</p>
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<p>A diameter subtends a right angle at the circumference: the central angle is \(180^\circ\), so the circumference angle is \(90^\circ\).</p>
<p>When stating a reason, identify the actual chord or arc involved. The vertex of an angle at the circumference must lie on the circle, and the centre must be given.</p>

The angle at the centre is twice the angle at the circumference standing on the same arc. Identify the arc before deciding whether the central angle is minor or reflex.

A diameter subtends a right angle at the circumference: the central angle is \(180^\circ\), so the circumference angle is \(90^\circ\).

When stating a reason, identify the actual chord or arc involved. The vertex of an angle at the circumference must lie on the circle, and the centre must be given.

Angles at the centre and circumference

Angles at the centre and circumference