1. 1 2 3 4 5 6 7 8 Isosceles triangles + perp. bisectors
Angle at center and at circumference 2
Angle in a semi circle 3
Angles in the same segment 4
Opposite angles in a cyclic quadrilateral 5
Right angle between a tangent and radius 6
Tangential lines the same length 7
Alternate segment theorem 8

2. Circle Property 1 Triangles formed using two radii will
form an isosceles
triangle.
The perpendicular
bisector of a chord
passes through the
the centre of the
circle.
Remember to spot isosceles triangles and perpendicular
bisectors in circle diagrams.

3. The angle at the centre is half the angle on the circumference.
Circle Property 2
The angle subtended by
an arc at the centre of
a circle, is twice the angle
subtended at the
circumference. x x 2x
The angle at the centre is half the angle on the circumference.

4. The angle in a semi-circle is a right angle.
Circle Property 3
Any angle subtended on
the circumference of a
semi- circle will be a
right angle angle. x
1800
The angle in a semi-circle is a right angle.

5. a and b are both “subtended” by the same chord
Circle Property 4 a a b
a and b are both “subtended” by the same chord
Bitesize

6. Opposite angles in a cyclic quadrilateral add to 1800.
Circle Property 5
Opposite angles in a cyclic
quadrilateral add up to 1800.
(A cyclic quadrilateral is a
4 sided shape with all four
points on the circumference
of a circle.) a x b
Opposite angles in a cyclic quadrilateral add to 1800.

7. A tangent to a circle is at right angles to its radius.
Circle Property 6 Q
The tangent to a circle
is perpendicular to the
radius drawn at the point
of contact.
OPQ = 900 P x O
A tangent to a circle is at right angles to its radius.

8. The tangents drawn from a point to a circle are equal in length.
Circle Property 7 Q
Two tangents drawn to
a circle from the same
point are equal in length.
QP = QR
QP = QR P x R O
The tangents drawn from a point to a circle are equal in length.

9. Circle Property 8 x y z y The angle between a
tangent and a chord drawn
at a point of contact is
equal to any angle in the
alternate segment. x y x z y
The angle between a tangent and a chord is equal to
the angle in the alternate segment.