Circle Theorems

• Theorem 1 - The line drawn from the centre of a circle to the midpoint of a chord is perpendicular to the chord
• Theorem 2 - The angle at the centre of a circle is twice the angle at the circumference.
• Theorem 3 - The angle in a semi-circle is a right angle.
• Theorem 4 - The triangle formed by 2 radi is an isosceles triangle
• Theorem 5 -Angles in the same segment are equal.
• Theorem 6 - Opposite angles in a cyclic quadrilateral add up to 180 degrees.
• Theorem 7 - The angle between a tangent and a chord is equal to the angle in the alternate segment.
• Theorem 8 - A tangent to a circle is perpendicular to the radius drawn from the point of contact.
• Theorem 9 - Tangents to a circle from an external point to the points of contact are equal in length.
• Theorem 10 - The line joining an external point to the centre of the circle bisects the angle between tangents.