Circle Theorems

The 9 cirlcle theorom rules...

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Rule 1

A TANGENT and a RADIUS meet at 90 DEGREES.

angle with a tangent (http://www.mathsrevision.net/sites/mathsrevision.net/files/Circle3.gif)

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Rule 2

2 RADII form an ISOSCELES TRIANGLE.

(http://mathsmad.com/circtheorumsint1.gif)

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Rule 3

The PERPENDICULAR BISECTOR of a CHORD passes through the CIRCLE'S CENTRE.

(perpendicular means it meets at 90 degrees)

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Rule 4

The ANGLE AT THE CENTRE of a circle is 2X the ANGLE AT THE CIRCUMFERENCE.

(http://mathsmad.com/circtheorumsint3.gif)

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Rule 5

The ANGLE in a SEMI-CIRCLE is 90 DEGREES.

This is because the angle at the centre of the circle is 180 degrees.

(http://mathsmad.com/circtheorumsint4.gif)

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Rule 6

ANGLES in the SAME SEGMENT are EQUAL.

(http://www.suffolkmaths.co.uk/pages/Top%20Activities/Teaching%20Techniques/Shape%20and%20Space/Circle%20Theorems/1_files/image004.jpg)

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Rule 7

OPPOSITE ANGLES in a CYCLIC QUADRILATERAL add up to 180 DEGREES.

(http://mathsmad.com/circtheorumsint7.gif)

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Rule 8

TANGENTS from the SAME POINT are EQUAL IN LENGTH.

From this, two congruent right-angled triangles can be made...

(http://mathsmad.com/circtheorumsint11.gif)

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Rule 9 (FINAL ONE!)

THE ALTERNATE SEGMENT THEOROM...

The ANGLE BETWEEN a TANGENT and CHORD is EQUAL to that of an ANGLE made from the cord in the OPPOSITE SEGMENT.

(http://mathsmad.com/circtheorumint12.gif)

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