Topic/SkillTopic:
Definition/Tips
Circle Theorems Example
Circle Angles in a semi-circle have a right angle
Theorem 1 at the circumference.
y=90°
x=180−90−38=52 °
Circle Opposite angles in a cyclic quadrilateral
Theorem 2 add up to 180°.
x=180−83=97 °
y=180−92=88 °
Circle The angle at the centre is twice the angle
Theorem 3 at the circumference.
x=104 ÷ 2=52 °
Circle Angles in the same segment are equal.
Theorem 4
x=42°
y=31 °
Circle A tangent is perpendicular to the radius
Theorem 5 at the point of contact.
y=5 cm(Pythagoras’ Theorem)
Circle Tangents from an external point at equal
Theorem 6 in length.
Mr A. Coleman Glyn School
Definition/Tips
Circle Theorems Example
Circle Angles in a semi-circle have a right angle
Theorem 1 at the circumference.
y=90°
x=180−90−38=52 °
Circle Opposite angles in a cyclic quadrilateral
Theorem 2 add up to 180°.
x=180−83=97 °
y=180−92=88 °
Circle The angle at the centre is twice the angle
Theorem 3 at the circumference.
x=104 ÷ 2=52 °
Circle Angles in the same segment are equal.
Theorem 4
x=42°
y=31 °
Circle A tangent is perpendicular to the radius
Theorem 5 at the point of contact.
y=5 cm(Pythagoras’ Theorem)
Circle Tangents from an external point at equal
Theorem 6 in length.
Mr A. Coleman Glyn School
