Year 10 Circle Theorems Flashcards
(18 cards)
Major arc
Longer arc of circle
Minor arc
Shorter arc of he circle
Radius
Line from centre to circumference of circle
Most important part of a circle
Sector
Slice of a circle
Minor segment
Smaller section of a circle separated by a chord
Major segment
Larger section of a circle separated by a chord
Tangent
Line passing that touches the circumference of the circle - stays outside the circle and continues
Diameter
Straight line splitting circle exactly in half
Double of radius
Alternate segment theorem
The angle that lies between a tangent and a chord is equal to the angle subtended by the same chord in the alternate segment.
. …/θ-…………
. ……/…………-………….
……/……………………-……
\…/————————-
. \ θ …………………..
. \………………
Angle at the centre theorem
Angle at centre is twice the angle at circumference
Angles in the same segment theorem
Angles in same segment are equal
. ………….
. ..|θ\…/θ|…
……..|…X…….|………
……..|./…\……|…..….
…….|/………\…|….….
. —————
. ………….
Angles in a semicircle theorem
Angle in a semicircle is 90 degrees
Chord bisector theorem
Perpendicular from the centre of a circle to a chord bisects the chord
(splits the chord into two equal parts)
Cyclic quadrilateral theorem
Opposite angles in a cyclic quadrilateral total 180°
All points of quadrilateral MUST touch circumference
Tangent of a circle theorem
A) The angle between a tangent and radius = 90 degrees
B) Tangents which meet at the same point are equal in length
Quadrilateral theorem
(Non Circle theorem)
Angles in any quadrilateral add up to 360°
Isosceles triangle theorem
(Non Circle theorem)
Base angles of an isosceles triangle are equal
Axiom
Something you don’t have to prove - basic building block of logic eg. 1 + 1 = 2
