Circle Theorems

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Description and Tags

Geometry & Trigonometry

Circles

IGCSE Maths: Extended

CIE

Geometry

Mathematimatimathiticas

Last updated 4:51 AM on 7/7/26
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10 Terms

1
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Angle at the centre

It is twice the angle at the circumference when both subtend the same arc.

<p>It is twice the angle at the circumference when both subtend the same arc.</p>
2
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Angle in a semicircle

It is always 90° (a right angle).

<p>It is always 90° (a right angle).</p>
3
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Angles in the same segment

They are always equal to each other.

<p>They are always equal to each other.</p>
4
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Opposite angles in a cyclic quadrilateral

They add up to 180° (supplementary).

<p>They add up to 180° (supplementary).</p>
5
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Tangent meets radius

They meet at 90° (perpendicular).

<p>They meet at 90° (perpendicular).</p>
6
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Tangents from a point

They are equal in length from that point to the circle.

<p>They are equal in length from that point to the circle.</p>
7
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Alternate segment theorem

The angle between the tangent and chord equals the angle in the opposite segment.

<p>The angle between the tangent and chord equals the angle in the opposite segment.</p>
8
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Perpendicular from centre to chord

It cuts the chord into two equal halves (bisects it).

<p>It cuts the chord into two equal halves (bisects it).</p>
9
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Equal chords

They subtend equal angles at the centre.

<p>They subtend equal angles at the centre.</p>
10
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Chord bisector

It is perpendicular to the chord.

<p>It is perpendicular to the chord.</p>