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CIRCLE THEOREMS



Angles Subtended on the same arc






Angles formed from two points on the circumference are equal to other
angles, in the same arc, formed from those two points.

Angle in a Semi-Circle






Angles formed by drawing lines from the ends of the diameter of a circle
to its…

Page 2

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Tangents

A tangent to a circle is a straight line which touches the circle at only
one point (so it does not cross the circle- it just touches it).

A tangent to a circle forms a right angle with the circle's radius, at the
point of contact of the tangent.…

Page 3

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Angle at the Centre






The angle formed at the centre of the circle by lines originating from
two points on the circle's circumference is double the angle formed on
the circumference of the circle by lines originating from the same points.
i.e. a = 2b.



Triangles Two Radii




As both…

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Chord Bisector




Chord (Cut in Two)



A Chord is any line drawn across a circle. Wherever it cuts it will always
be 90 Degrees)



Cyclic Quadrilateral




A Cyclic Quadrilateral is a 4-sided shape with every corner touching the
circle. Both pairs of opposite angles add up to 180

Page 5

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ALTERNATE SEGMENT THEOREM




This diagram shows the alternate segment theorem. In short, the red angles are equal to each
other and the green angles are equal to each other.
PROOF
You may have to be able to prove the alternate segment theorem:




We use facts about related angles:
A tangent…

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