Circle theorem powerpoint updated
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Transcript of Circle theorem powerpoint updated
![Page 1: Circle theorem powerpoint updated](https://reader036.fdocuments.us/reader036/viewer/2022062503/588844eb1a28ab7a298b6fff/html5/thumbnails/1.jpg)
CIRCLE THEOREM
Remember to look for “basics”•Angles in a triangle sum to 1800
•Angles on a line sum to 1800
• Isosceles triangles (radius)•Angles about a point sum to 3600
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Name parts of a circle
Diameterradius
chord
tangentCircumference
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400
800
THEOREM 1: ANGLE at the CENTRE of the CIRCLE is twice the angle at the circumference subtended by the same arc.
MUST BE THE CENTER
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THIS RULE CAN BE HARD TO
SPOT…..
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THIS IS THE ONE MOST PEOPLE DON’T SEE......
1150
2300
MUST BE THE CENTER
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400
800
LOOKS DIFFEREN
T BUT STILL THE CENTRE
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SPECIAL CASE OF THE SAME RULE……… BUT MAKES A RULE IN ITS OWN RIGHT!!
900
1800
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THEOREM 2: Every angle at the circumference of a SEMICIRCLE, that is subtended by the diameter of the semi-circle is a right angle.
900
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THEOREM 3: Opposite angles sum to 180 in a cyclic quadrilateral
CYCLIC QUADRILATEARA
L MUST touch the circumference at all four vertices
910
890
700
1100
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RULE 4: Angles at the circumference in the same SEGMENT of a circle are equal
The two angles marked are the same
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= the same angle
RULE 4: Angles at the circumference in the same SEGMENT of a circle are equal
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• A tangent is a line that touches a circle at one point only. This point is called the point of contact
• A chord is a line that joins two points on the circumference.
chord
tangent
TANGENTS AND CHORDS
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THEOREM 4: Angles at the circumference in the same SEGMENT of a circle are equal
NOTE: Will lead you to SIMILAR triangles (one is an enlargement of the other….)
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Theorem 5 – A tangent is perpendicular to a radius
radius
tangent900
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Theorem 6 – Tangents to a circle from the same point are equal in
length
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Theorem 7 – The line joining an external point to the centre of a circle bisects the angle
between the tangents
700350
350
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Theorem 5&7 – combined can help you find the missing angles…..
700350
350
900
900
xy
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THEOREM 8 – A RADIUS BISECTS A CHORD AT 900
radius chord900
And the chord will be cut perfectly in half.
MIDPOINT OF THE CHORD
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THEOREM 9 – ALTERNATE ANGLE THEOREM
Need a tangent,and a triangle that joins the tangent and two
other points on the circumference of the circle.
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THEOREM 9 – ALTERNATE ANGLE THEOREM
Opposite angles are the same
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THEOREM 9 – ALTERNATE ANGLE THEOREM
The angle between a tangent and a chord,Is equal to the angle in the alternate segment