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Title: GCSE Circle Theorems
Description: Circle Theorems for GCSE in a concise but thorough way. Easy to understand diagrams and text.
Description: Circle Theorems for GCSE in a concise but thorough way. Easy to understand diagrams and text.
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Circle Theorems
Circle Terminology
A circle is a 2-dimensional shape made by drawing a curve that is always the
same distance from a fixed point
...
A chord is a straight line segment whose endpoints both lie on the circle
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The length of a diameter is double that of a radius
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A tangent is a line which touches a circle once on its circumference
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The angle at the circumference in a semicircle is a right angle
...
)
In this diagram we can see that the green square is a right angle or 90 degrees
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Because they are isosceles, the size of the base angles are equal
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Test Question
1
...
2
...
This famous theorem is can be
dedicated to the Greek
mathematician Thales
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The angle at the circumference is half as big as the angle in the
centre
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Proof
When the arc is a semicircle, like above, the angle at the centre is a straight angle of 180
degrees and the angle at the circumference is a right angle (which is half)
...
Test Questions
1
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Angles in the same segment are equal
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4
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5
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When there are four points, we can always draw a circle through any three of them (as
long as they are not collinear), but the circle will only pass through the fourth point in
special cases
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In this diagram the two orange angles add up to 180 degrees and the two green angles
add up to 180 degrees
...
6
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You can see a demonstration of circle theorem number five here as well
...
You may also be able to use sin, cosine, or right angled
triangle theorems to work out other angles or lengths from these triangles
...
Alternate Segment Theorem - the angle between a tangent and
a chord is the same as the angle in the alternate segment
...
The easiest way to find
one is by looking for a triangle with one of
its corners (vertices) touching a tangent
Title: GCSE Circle Theorems
Description: Circle Theorems for GCSE in a concise but thorough way. Easy to understand diagrams and text.
Description: Circle Theorems for GCSE in a concise but thorough way. Easy to understand diagrams and text.