Year 10 Circle Theorems

Question 1

Major arc

Answer 1

Longer arc of circle

Question 2

Minor arc

Answer 2

Shorter arc of he circle

Question 3

Radius

Answer 3

Line from centre to circumference of circle
Most important part of a circle

Question 4

Sector

Answer 4

Slice of a circle

Question 5

Minor segment

Answer 5

Smaller section of a circle separated by a chord

Question 6

Major segment

Answer 6

Larger section of a circle separated by a chord

Question 7

Tangent

Answer 7

Line passing that touches the circumference of the circle - stays outside the circle and continues

Question 8

Diameter

Answer 8

Straight line splitting circle exactly in half
Double of radius

Question 9

Alternate segment theorem

Answer 9

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 …………………..
. \………………

Question 10

Angle at the centre theorem

Answer 10

Angle at centre is twice the angle at circumference

Question 11

Angles in the same segment theorem

Answer 11

Angles in same segment are equal

. ………….
. ..|θ\…/θ|…
……..|…X…….|………
……..|./…\……|…..….
…….|/………\…|….….
. —————
. ………….

Question 12

Angles in a semicircle theorem

Answer 12

Angle in a semicircle is 90 degrees

Question 13

Chord bisector theorem

Answer 13

Perpendicular from the centre of a circle to a chord bisects the chord
(splits the chord into two equal parts)

Question 14

Cyclic quadrilateral theorem

Answer 14

Opposite angles in a cyclic quadrilateral total 180°
All points of quadrilateral MUST touch circumference

Question 15

Tangent of a circle theorem

Answer 15

A) The angle between a tangent and radius = 90 degrees
B) Tangents which meet at the same point are equal in length

Question 16

Quadrilateral theorem
(Non Circle theorem)

Answer 16

Angles in any quadrilateral add up to 360°

Question 17

Isosceles triangle theorem
(Non Circle theorem)

Answer 17

Base angles of an isosceles triangle are equal

Question 18

Axiom

Answer 18

Something you don’t have to prove - basic building block of logic eg. 1 + 1 = 2