EUCLIDEAN
CIRCLE GEOMETRY
THEOREM 1
Reason: ⟂ Line from centre to midpt chord
The line segment joining the centre of a circle to the midpoint of a chord is
perpendicular to the chord to a chord bisects the chord.
Proof:
,EUCLIDEAN
CIRCLE GEOMETRY
THEOREM 2
Reason: ∠ at centre = 2 x ∠ at circum
The angle subtended by an arc at the centre of the circle is twice the angle the
arc subtends at any point on the circumference of the circle.
Proof:
, EUCLIDEAN
CIRCLE GEOMETRY
THEOREM 3
Reason: ∠ in semi-circle
The angle subtended by the diameter at the circumference of a circle is a right
angle.
Diagram:
CIRCLE GEOMETRY
THEOREM 1
Reason: ⟂ Line from centre to midpt chord
The line segment joining the centre of a circle to the midpoint of a chord is
perpendicular to the chord to a chord bisects the chord.
Proof:
,EUCLIDEAN
CIRCLE GEOMETRY
THEOREM 2
Reason: ∠ at centre = 2 x ∠ at circum
The angle subtended by an arc at the centre of the circle is twice the angle the
arc subtends at any point on the circumference of the circle.
Proof:
, EUCLIDEAN
CIRCLE GEOMETRY
THEOREM 3
Reason: ∠ in semi-circle
The angle subtended by the diameter at the circumference of a circle is a right
angle.
Diagram:
