Maths - Circle Theorems Notes

Maths - Circle Theorems Notes

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  • Created by: Frenchie
  • Created on: 09-06-11 19:38
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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 circumference form a right angle. So c is a right angle.

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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.…read more

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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.…read more

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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.…read more

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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.
You may have to be able to prove the alternate segment theorem:
We use facts about related angles:
A tangent makes an angle of 90 degrees with the radius of a circle, so we know that OAC + x =
The angle in a semicircle is 90, so BCA = 90.…read more


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